Property of topological spaces

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This article is about a general term. A list of important particular cases (instances) is available at Category:Properties of topological spaces

Definition

A property of topological spaces is a rule from the collection of topological spaces to the two-element set (True, False), such that if two spaces are homeomorphic, they get mapped to the same thing.

The topological spaces that get mapped to True are said to satisfy the property or have the property, and the topological spaces that get mapped to False are said to not satisfy the property or not have the property.