# Property of topological spaces

From Topospaces

*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.