Name for a one-dimensional domain/set that is topologically like a circle?

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Is there a special name for a continuous one-dimensional domain/set that wraps around on itself?



Example 1: The set of unit vectors in $mathbbR^2$.



Example 2: The set of points on a square.



Example 3: $[0,2pi)$ with an additional link between $0$ and $2pi$.










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  • 1




    "Connected, compact 1 dimensional manifold" describes what you want.
    – Mike Earnest
    Sep 10 at 13:19







  • 3




    Why not "a topological circle"?
    – Mees de Vries
    Sep 10 at 13:26






  • 1




    You could say $[0,1]$ is a connected, compact 1 dimensional manifold with boundary. The other comments do a better job answering your question, topological circle is the best terminology.
    – Mike Earnest
    Sep 10 at 13:39






  • 1




    A set $S$ homeomorphic to a circle.
    – Thomas
    Sep 10 at 15:03






  • 1




    It needs to be one-holed in some sense (if you don't want to allow multiwraps).
    – mathreadler
    Sep 10 at 15:41















up vote
0
down vote

favorite












Is there a special name for a continuous one-dimensional domain/set that wraps around on itself?



Example 1: The set of unit vectors in $mathbbR^2$.



Example 2: The set of points on a square.



Example 3: $[0,2pi)$ with an additional link between $0$ and $2pi$.










share|cite|improve this question



















  • 1




    "Connected, compact 1 dimensional manifold" describes what you want.
    – Mike Earnest
    Sep 10 at 13:19







  • 3




    Why not "a topological circle"?
    – Mees de Vries
    Sep 10 at 13:26






  • 1




    You could say $[0,1]$ is a connected, compact 1 dimensional manifold with boundary. The other comments do a better job answering your question, topological circle is the best terminology.
    – Mike Earnest
    Sep 10 at 13:39






  • 1




    A set $S$ homeomorphic to a circle.
    – Thomas
    Sep 10 at 15:03






  • 1




    It needs to be one-holed in some sense (if you don't want to allow multiwraps).
    – mathreadler
    Sep 10 at 15:41













up vote
0
down vote

favorite









up vote
0
down vote

favorite











Is there a special name for a continuous one-dimensional domain/set that wraps around on itself?



Example 1: The set of unit vectors in $mathbbR^2$.



Example 2: The set of points on a square.



Example 3: $[0,2pi)$ with an additional link between $0$ and $2pi$.










share|cite|improve this question















Is there a special name for a continuous one-dimensional domain/set that wraps around on itself?



Example 1: The set of unit vectors in $mathbbR^2$.



Example 2: The set of points on a square.



Example 3: $[0,2pi)$ with an additional link between $0$ and $2pi$.







general-topology terminology






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share|cite|improve this question













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edited Sep 10 at 13:20

























asked Sep 10 at 13:14









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  • 1




    "Connected, compact 1 dimensional manifold" describes what you want.
    – Mike Earnest
    Sep 10 at 13:19







  • 3




    Why not "a topological circle"?
    – Mees de Vries
    Sep 10 at 13:26






  • 1




    You could say $[0,1]$ is a connected, compact 1 dimensional manifold with boundary. The other comments do a better job answering your question, topological circle is the best terminology.
    – Mike Earnest
    Sep 10 at 13:39






  • 1




    A set $S$ homeomorphic to a circle.
    – Thomas
    Sep 10 at 15:03






  • 1




    It needs to be one-holed in some sense (if you don't want to allow multiwraps).
    – mathreadler
    Sep 10 at 15:41













  • 1




    "Connected, compact 1 dimensional manifold" describes what you want.
    – Mike Earnest
    Sep 10 at 13:19







  • 3




    Why not "a topological circle"?
    – Mees de Vries
    Sep 10 at 13:26






  • 1




    You could say $[0,1]$ is a connected, compact 1 dimensional manifold with boundary. The other comments do a better job answering your question, topological circle is the best terminology.
    – Mike Earnest
    Sep 10 at 13:39






  • 1




    A set $S$ homeomorphic to a circle.
    – Thomas
    Sep 10 at 15:03






  • 1




    It needs to be one-holed in some sense (if you don't want to allow multiwraps).
    – mathreadler
    Sep 10 at 15:41








1




1




"Connected, compact 1 dimensional manifold" describes what you want.
– Mike Earnest
Sep 10 at 13:19





"Connected, compact 1 dimensional manifold" describes what you want.
– Mike Earnest
Sep 10 at 13:19





3




3




Why not "a topological circle"?
– Mees de Vries
Sep 10 at 13:26




Why not "a topological circle"?
– Mees de Vries
Sep 10 at 13:26




1




1




You could say $[0,1]$ is a connected, compact 1 dimensional manifold with boundary. The other comments do a better job answering your question, topological circle is the best terminology.
– Mike Earnest
Sep 10 at 13:39




You could say $[0,1]$ is a connected, compact 1 dimensional manifold with boundary. The other comments do a better job answering your question, topological circle is the best terminology.
– Mike Earnest
Sep 10 at 13:39




1




1




A set $S$ homeomorphic to a circle.
– Thomas
Sep 10 at 15:03




A set $S$ homeomorphic to a circle.
– Thomas
Sep 10 at 15:03




1




1




It needs to be one-holed in some sense (if you don't want to allow multiwraps).
– mathreadler
Sep 10 at 15:41





It needs to be one-holed in some sense (if you don't want to allow multiwraps).
– mathreadler
Sep 10 at 15:41
















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