Topologically star-like space

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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

Definition

A non-empty topological space is termed topologically star-like if it is homeomorphic to a star-like subset of Euclidean space (Where the Euclidean space is possibly infinite-dimensional), where the latter is endowed with the subspace topology from Euclidean space.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
topologically convex space homemorphic to a convex subset of Euclidean space follows from convex implies star-like  ? |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
contractible space has a contracting homotopy star-like implies contractible |FULL LIST, MORE INFO
semi-suddenly contractible space has a semi-sudden contracting homotopy star-like implies contractible |FULL LIST, MORE INFO
SDR-contractible space has a contracting homotopy that is a deformation retraction star-like implies contractible |FULL LIST, MORE INFO