# Compactly nondegenerate space

From Topospaces

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

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## Definition

### Symbol-free definition

A topological space is termed **compactly nondegenerate** if every point is contained in an open set, whose closure is compact, and such that the inclusion of the union of the point with the boundary of the open set, inside the closure, is a cofibration.

## Facts

- If, in a Hausdorff space, every point is contained in a compactly nondegenerate open set, then the whole space is compactly nondegenerate.
- Euclidean space is compactly nondegenerate. This gives a proof that manifolds are nondegenerate, in fact they are compactly nondegenerate.