Definition:Hereditary Property (Topology)
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Let $\xi$ be a property whose domain is the set of all topological spaces.
Then $\xi$ is a hereditary property if and only if:
- $\map \xi X \implies \map \xi Y$
where $Y$ is a subspace of $X$.
That is, whenever a topological space has $\xi$, then so does any subspace.
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $1$: General Introduction
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): hereditary: 3. (of a topological property)
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): hereditary property