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homeomorphism
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(Definition)
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A homeomorphism  of topological spaces is a continuous, bijective map such that  is also continuous. We also say that two spaces are homeomorphic if such a map exists.
If two topological spaces are homeomorphic, they are topologically equivalent -- using the techniques of topology, there is no way of distinguishing one space from the other.
An autohomeomorphism (also known as a self-homeomorphism) is a homeomorphism from a topological space to itself.
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"homeomorphism" is owned by rspuzio. [ full author list (2) | owner history (1) ]
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(view preamble)
See Also: homeotopy, crosscap slide, Alexander trick
| Other names: |
topological equivalence, topologically equivalent |
| Also defines: |
homeomorphic, autohomeomorphism, auto-homeomorphism, self-homeomorphism |
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Cross-references: map, bijective, continuous, topological spaces
There are 127 references to this entry.
This is version 12 of homeomorphism, born on 2001-11-16, modified 2006-10-14.
Object id is 912, canonical name is Homeomorphism.
Accessed 19589 times total.
Classification:
| AMS MSC: | 54C05 (General topology :: Maps and general types of spaces defined by maps :: Continuous maps) |
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Pending Errata and Addenda
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