# Triangulable manifold

From Topospaces

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

## Contents

## 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 |