Triangulable manifold

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This article describes a property of topological spaces obtained as a conjunction of the following two properties: manifold and polyhedron

Definition

A triangulable manifold is a topological space that is both a manifold and a polyhedron. In other words, it is a manifold that admits a triangulation, i.e., is homeomorphic to the geometric realization of a simplicial complex.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
manifold admitting a PL structure admits the structure of a PL manifold (direct) |FULL LIST, MORE INFO
differentiable manifold manifold that admits the structure of a differential manifold (via PL structure) (via PL structure) |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
manifold |FULL LIST, MORE INFO
polyhedron triangulable space, i.e., geometric realization of a simplicial complex |FULL LIST, MORE INFO
CW-space |FULL LIST, MORE INFO