Definition:Topological Property

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Definition

Let $P$ be a property whose domain is the set of all topological spaces.

Suppose that whenever $P \left({T}\right)$ holds, then so does $P \left({T'}\right)$, where $T$ and $T'$ are topological spaces which are homeomorphic.


Then $P$ is known as a topological property.


Loosely, a topological property is one which is preserved under homeomorphism.


Also known as

  • A topological property is also known as a topological invariant.


Also see


Sources