Triangulable manifold
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 |