How to Prove cantor Set is Perfect easily? [duplicate]
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A proof that the Cantor set is Perfect
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Can some one tell me how to prove Cantor set is perfect?
general-topology
asked Aug 20 at 6:16
Lahiru Dhananjaya
92
marked as duplicate by José Carlos Santos, Shailesh, A. Pongrácz, Theo Bendit, Siong Thye Goh Aug 20 at 7:09
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This question already has an answer here:
A proof that the Cantor set is Perfect
1 answer
Can some one tell me how to prove Cantor set is perfect?
general-topology
asked Aug 20 at 6:16
Lahiru Dhananjaya
92
marked as duplicate by José Carlos Santos, Shailesh, A. Pongrácz, Theo Bendit, Siong Thye Goh Aug 20 at 7:09
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
1
You can characterise elements of the Cantor sets by their Ternary expansions, particularly its the numbers in $[0, 1]$ with ternary expansions consisting only of $0$ and $2$. Simply modify one of the trits sufficiently far along the expansion, and you can find another element of the Cantor set that is within any $varepsilon > 0$ distance.
– Theo Bendit
Aug 20 at 6:25
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up vote
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up vote
0
down vote
favorite
This question already has an answer here:
A proof that the Cantor set is Perfect
1 answer
Can some one tell me how to prove Cantor set is perfect?
general-topology
asked Aug 20 at 6:16
Lahiru Dhananjaya
92
This question already has an answer here:
A proof that the Cantor set is Perfect
1 answer
Can some one tell me how to prove Cantor set is perfect?
This question already has an answer here:
A proof that the Cantor set is Perfect
1 answer
general-topology
asked Aug 20 at 6:16
Lahiru Dhananjaya
92
asked Aug 20 at 6:16
Lahiru Dhananjaya
92
asked Aug 20 at 6:16
Lahiru Dhananjaya
92
asked Aug 20 at 6:16
Lahiru Dhananjaya
92
92
marked as duplicate by José Carlos Santos, Shailesh, A. Pongrácz, Theo Bendit, Siong Thye Goh Aug 20 at 7:09
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by José Carlos Santos, Shailesh, A. Pongrácz, Theo Bendit, Siong Thye Goh Aug 20 at 7:09
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
1
You can characterise elements of the Cantor sets by their Ternary expansions, particularly its the numbers in $[0, 1]$ with ternary expansions consisting only of $0$ and $2$. Simply modify one of the trits sufficiently far along the expansion, and you can find another element of the Cantor set that is within any $varepsilon > 0$ distance.
– Theo Bendit
Aug 20 at 6:25
add a comment |Â
1
You can characterise elements of the Cantor sets by their Ternary expansions, particularly its the numbers in $[0, 1]$ with ternary expansions consisting only of $0$ and $2$. Simply modify one of the trits sufficiently far along the expansion, and you can find another element of the Cantor set that is within any $varepsilon > 0$ distance.
– Theo Bendit
Aug 20 at 6:25
1
1
You can characterise elements of the Cantor sets by their Ternary expansions, particularly its the numbers in $[0, 1]$ with ternary expansions consisting only of $0$ and $2$. Simply modify one of the trits sufficiently far along the expansion, and you can find another element of the Cantor set that is within any $varepsilon > 0$ distance.
– Theo Bendit
Aug 20 at 6:25
You can characterise elements of the Cantor sets by their Ternary expansions, particularly its the numbers in $[0, 1]$ with ternary expansions consisting only of $0$ and $2$. Simply modify one of the trits sufficiently far along the expansion, and you can find another element of the Cantor set that is within any $varepsilon > 0$ distance.
– Theo Bendit
Aug 20 at 6:25
add a comment |Â
1 Answer
1
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No. That is, not "easily".
For a proof, not necessarily an easy one, see here:
A proof that the Cantor set is Perfect
answered Aug 20 at 6:23
uniquesolution
8,251823
Thanks a lot. This gives better and easy view on proving above.
– Lahiru Dhananjaya
Aug 20 at 6:31
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
No. That is, not "easily".
For a proof, not necessarily an easy one, see here:
A proof that the Cantor set is Perfect
answered Aug 20 at 6:23
uniquesolution
8,251823
Thanks a lot. This gives better and easy view on proving above.
– Lahiru Dhananjaya
Aug 20 at 6:31
add a comment |Â
up vote
0
down vote
No. That is, not "easily".
For a proof, not necessarily an easy one, see here:
A proof that the Cantor set is Perfect
answered Aug 20 at 6:23
uniquesolution
8,251823
Thanks a lot. This gives better and easy view on proving above.
– Lahiru Dhananjaya
Aug 20 at 6:31
add a comment |Â
up vote
0
down vote
up vote
0
down vote
No. That is, not "easily".
For a proof, not necessarily an easy one, see here:
A proof that the Cantor set is Perfect
answered Aug 20 at 6:23
uniquesolution
8,251823
No. That is, not "easily".
For a proof, not necessarily an easy one, see here:
A proof that the Cantor set is Perfect
answered Aug 20 at 6:23
uniquesolution
8,251823
answered Aug 20 at 6:23
uniquesolution
8,251823
answered Aug 20 at 6:23
uniquesolution
8,251823
answered Aug 20 at 6:23
uniquesolution
8,251823
8,251823
Thanks a lot. This gives better and easy view on proving above.
– Lahiru Dhananjaya
Aug 20 at 6:31
add a comment |Â
Thanks a lot. This gives better and easy view on proving above.
– Lahiru Dhananjaya
Aug 20 at 6:31
Thanks a lot. This gives better and easy view on proving above.
– Lahiru Dhananjaya
Aug 20 at 6:31
Thanks a lot. This gives better and easy view on proving above.
– Lahiru Dhananjaya
Aug 20 at 6:31
add a comment |Â
1
You can characterise elements of the Cantor sets by their Ternary expansions, particularly its the numbers in $[0, 1]$ with ternary expansions consisting only of $0$ and $2$. Simply modify one of the trits sufficiently far along the expansion, and you can find another element of the Cantor set that is within any $varepsilon > 0$ distance.
– Theo Bendit
Aug 20 at 6:25