What is the need of topology? [closed]

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I am not getting that what is the actual notion of topology and what are the best books of topology for beginner.



I always try to visualise the topology but I fail. I am not getting any idea.



How do I study topology?



Please explain the right way.




general-topology soft-question




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closed as unclear what you're asking by Shaun, John Douma, José Carlos Santos, Andres Mejia, Alex Provost Aug 8 at 17:48


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.










  • 3




    The question in the title seems different from the question in your answer. Still, I think Willard is one of the bast math texts I ever used. I took general topology as a reading course, never met with the professor, and just read Willard. I had no problems.
    – saulspatz
    Aug 8 at 17:37







  • 1




    Are you an underdraduate? self learner ? tell us some more info, please....
    – dmtri
    Aug 8 at 17:39










  • I believe it broadly attempts to answer the question "How are things connected?", and often uses the idea of 'invariance'. Contrasting examples might include: topologies of the physical universe, network topologies, topological dynamical systems and molecular topologies.
    – D. G.
    Aug 8 at 17:59










  • Topology is around the terms point, neighborhood (of a point), open and closed sets, continuous function..
    – Berci
    Aug 8 at 18:39














up vote
-2
down vote

favorite
1












I am not getting that what is the actual notion of topology and what are the best books of topology for beginner.



I always try to visualise the topology but I fail. I am not getting any idea.



How do I study topology?



Please explain the right way.




general-topology soft-question




share|cite|improve this question














closed as unclear what you're asking by Shaun, John Douma, José Carlos Santos, Andres Mejia, Alex Provost Aug 8 at 17:48


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.










  • 3




    The question in the title seems different from the question in your answer. Still, I think Willard is one of the bast math texts I ever used. I took general topology as a reading course, never met with the professor, and just read Willard. I had no problems.
    – saulspatz
    Aug 8 at 17:37







  • 1




    Are you an underdraduate? self learner ? tell us some more info, please....
    – dmtri
    Aug 8 at 17:39










  • I believe it broadly attempts to answer the question "How are things connected?", and often uses the idea of 'invariance'. Contrasting examples might include: topologies of the physical universe, network topologies, topological dynamical systems and molecular topologies.
    – D. G.
    Aug 8 at 17:59










  • Topology is around the terms point, neighborhood (of a point), open and closed sets, continuous function..
    – Berci
    Aug 8 at 18:39












up vote
-2
down vote

favorite
1









up vote
-2
down vote

favorite
1






1





I am not getting that what is the actual notion of topology and what are the best books of topology for beginner.



I always try to visualise the topology but I fail. I am not getting any idea.



How do I study topology?



Please explain the right way.




general-topology soft-question




share|cite|improve this question














I am not getting that what is the actual notion of topology and what are the best books of topology for beginner.



I always try to visualise the topology but I fail. I am not getting any idea.



How do I study topology?



Please explain the right way.





general-topology soft-question





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 8 at 17:29









Shaun

7,40592972




7,40592972










asked Aug 8 at 17:28









Ajeet singh

22




22




closed as unclear what you're asking by Shaun, John Douma, José Carlos Santos, Andres Mejia, Alex Provost Aug 8 at 17:48


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.






closed as unclear what you're asking by Shaun, John Douma, José Carlos Santos, Andres Mejia, Alex Provost Aug 8 at 17:48


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.









  • 3




    The question in the title seems different from the question in your answer. Still, I think Willard is one of the bast math texts I ever used. I took general topology as a reading course, never met with the professor, and just read Willard. I had no problems.
    – saulspatz
    Aug 8 at 17:37







  • 1




    Are you an underdraduate? self learner ? tell us some more info, please....
    – dmtri
    Aug 8 at 17:39










  • I believe it broadly attempts to answer the question "How are things connected?", and often uses the idea of 'invariance'. Contrasting examples might include: topologies of the physical universe, network topologies, topological dynamical systems and molecular topologies.
    – D. G.
    Aug 8 at 17:59










  • Topology is around the terms point, neighborhood (of a point), open and closed sets, continuous function..
    – Berci
    Aug 8 at 18:39












  • 3




    The question in the title seems different from the question in your answer. Still, I think Willard is one of the bast math texts I ever used. I took general topology as a reading course, never met with the professor, and just read Willard. I had no problems.
    – saulspatz
    Aug 8 at 17:37







  • 1




    Are you an underdraduate? self learner ? tell us some more info, please....
    – dmtri
    Aug 8 at 17:39










  • I believe it broadly attempts to answer the question "How are things connected?", and often uses the idea of 'invariance'. Contrasting examples might include: topologies of the physical universe, network topologies, topological dynamical systems and molecular topologies.
    – D. G.
    Aug 8 at 17:59










  • Topology is around the terms point, neighborhood (of a point), open and closed sets, continuous function..
    – Berci
    Aug 8 at 18:39







3




3




The question in the title seems different from the question in your answer. Still, I think Willard is one of the bast math texts I ever used. I took general topology as a reading course, never met with the professor, and just read Willard. I had no problems.
– saulspatz
Aug 8 at 17:37





The question in the title seems different from the question in your answer. Still, I think Willard is one of the bast math texts I ever used. I took general topology as a reading course, never met with the professor, and just read Willard. I had no problems.
– saulspatz
Aug 8 at 17:37





1




1




Are you an underdraduate? self learner ? tell us some more info, please....
– dmtri
Aug 8 at 17:39




Are you an underdraduate? self learner ? tell us some more info, please....
– dmtri
Aug 8 at 17:39












I believe it broadly attempts to answer the question "How are things connected?", and often uses the idea of 'invariance'. Contrasting examples might include: topologies of the physical universe, network topologies, topological dynamical systems and molecular topologies.
– D. G.
Aug 8 at 17:59




I believe it broadly attempts to answer the question "How are things connected?", and often uses the idea of 'invariance'. Contrasting examples might include: topologies of the physical universe, network topologies, topological dynamical systems and molecular topologies.
– D. G.
Aug 8 at 17:59












Topology is around the terms point, neighborhood (of a point), open and closed sets, continuous function..
– Berci
Aug 8 at 18:39




Topology is around the terms point, neighborhood (of a point), open and closed sets, continuous function..
– Berci
Aug 8 at 18:39










1 Answer
1






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up vote
1
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In my opinion topology is a relaxed geometry. Circles are too perfect, too exact, but a closed curve which is topologically identical ( homeomorphic ) to a circle will do for most applications.



For example in complex variables we learn about the Cauchy integral formula, which is an integral around a simple closed curve and the answer will not change as long as your curve is a closed and simple that is homeomorphic to a circle.



The real world is not perfectly geometric for example the earth is not a perfect sphere but you can say it is a topologically equivalent of a sphere.



When you draw a rectangle with hand, you get something which is more than likely not a rectangle but very close to one and you can prove your problems with your not so perfect rectangle.



Surprisingly, these days Topology is applied in science and statistics. So Topology is not just a pure branch of mathematics any more.






share|cite|improve this answer




















  • Examples of Of such applications?
    – William Elliot
    Aug 8 at 19:37


















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
1
down vote













In my opinion topology is a relaxed geometry. Circles are too perfect, too exact, but a closed curve which is topologically identical ( homeomorphic ) to a circle will do for most applications.



For example in complex variables we learn about the Cauchy integral formula, which is an integral around a simple closed curve and the answer will not change as long as your curve is a closed and simple that is homeomorphic to a circle.



The real world is not perfectly geometric for example the earth is not a perfect sphere but you can say it is a topologically equivalent of a sphere.



When you draw a rectangle with hand, you get something which is more than likely not a rectangle but very close to one and you can prove your problems with your not so perfect rectangle.



Surprisingly, these days Topology is applied in science and statistics. So Topology is not just a pure branch of mathematics any more.






share|cite|improve this answer




















  • Examples of Of such applications?
    – William Elliot
    Aug 8 at 19:37















up vote
1
down vote













In my opinion topology is a relaxed geometry. Circles are too perfect, too exact, but a closed curve which is topologically identical ( homeomorphic ) to a circle will do for most applications.



For example in complex variables we learn about the Cauchy integral formula, which is an integral around a simple closed curve and the answer will not change as long as your curve is a closed and simple that is homeomorphic to a circle.



The real world is not perfectly geometric for example the earth is not a perfect sphere but you can say it is a topologically equivalent of a sphere.



When you draw a rectangle with hand, you get something which is more than likely not a rectangle but very close to one and you can prove your problems with your not so perfect rectangle.



Surprisingly, these days Topology is applied in science and statistics. So Topology is not just a pure branch of mathematics any more.






share|cite|improve this answer




















  • Examples of Of such applications?
    – William Elliot
    Aug 8 at 19:37













up vote
1
down vote










up vote
1
down vote









In my opinion topology is a relaxed geometry. Circles are too perfect, too exact, but a closed curve which is topologically identical ( homeomorphic ) to a circle will do for most applications.



For example in complex variables we learn about the Cauchy integral formula, which is an integral around a simple closed curve and the answer will not change as long as your curve is a closed and simple that is homeomorphic to a circle.



The real world is not perfectly geometric for example the earth is not a perfect sphere but you can say it is a topologically equivalent of a sphere.



When you draw a rectangle with hand, you get something which is more than likely not a rectangle but very close to one and you can prove your problems with your not so perfect rectangle.



Surprisingly, these days Topology is applied in science and statistics. So Topology is not just a pure branch of mathematics any more.






share|cite|improve this answer












In my opinion topology is a relaxed geometry. Circles are too perfect, too exact, but a closed curve which is topologically identical ( homeomorphic ) to a circle will do for most applications.



For example in complex variables we learn about the Cauchy integral formula, which is an integral around a simple closed curve and the answer will not change as long as your curve is a closed and simple that is homeomorphic to a circle.



The real world is not perfectly geometric for example the earth is not a perfect sphere but you can say it is a topologically equivalent of a sphere.



When you draw a rectangle with hand, you get something which is more than likely not a rectangle but very close to one and you can prove your problems with your not so perfect rectangle.



Surprisingly, these days Topology is applied in science and statistics. So Topology is not just a pure branch of mathematics any more.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Aug 8 at 17:44









Mohammad Riazi-Kermani

28.1k41852




28.1k41852











  • Examples of Of such applications?
    – William Elliot
    Aug 8 at 19:37

















  • Examples of Of such applications?
    – William Elliot
    Aug 8 at 19:37
















Examples of Of such applications?
– William Elliot
Aug 8 at 19:37





Examples of Of such applications?
– William Elliot
Aug 8 at 19:37



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