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homeomorphic 数学

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英语

A 2-cell embedding or map is an embedding in which every face is homeomorphic to an open disk. en.wikipedia.org

The clique complex of the graph is then homeomorphic to the surface. en.wikipedia.org

A space is metrizable if it is homeomorphic to a metric space. en.wikipedia.org

Care must be taken insofar as two tori are always homeomorphic, but in general not biholomorphic to each other. en.wikipedia.org

Intuitively, two spaces are homeomorphic if one can be deformed into the other without cutting or gluing. en.wikipedia.org

The correct version in this case is that if two knots have complements which are orientation-preserving homeomorphic, then they are isotopic. en.wikipedia.org

A precise definition of homeomorphic, involving a continuous function with a continuous inverse, is necessarily more technical. en.wikipedia.org

There are various properties that uniquely specify them; for instance, all unbounded, connected, and separable order topologies are necessarily homeomorphic to the reals. en.wikipedia.org

But a unit-square has no cut-point, and so can not be homeomorphic to the unit interval, in which all points except the endpoints are cut-points. en.wikipedia.org

Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same. en.wikipedia.org

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