Homeomorphic

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Definition

Two topological spaces, [ilmath](X,\mathcal{ J })[/ilmath] and [ilmath](Y,\mathcal{ K })[/ilmath], are said to be homeomorphic if there exists a homeomorphism between them. Recall a homeomorphism a continuous bijection with a continuous inverse.

A homeomorphism is an isomorphism in the TOP category, as such it is an equivalence relation on the morphisms (which are continuous maps) between [ilmath](X,\mathcal{ J })[/ilmath] and [ilmath](Y,\mathcal{ K })[/ilmath].