Category:Topological Manifolds with Boundary

This category contains definitions related to Topological Manifolds with Boundary.
Related results can be found in Category:Topological Manifolds with Boundary.

Let $\R^n$ denote the $n$-dimensional Euclidean space.

Let $\H^n$ denote the $n$-dimensional closed upper half-space of $\R^n$.

A $d$-dimensional topological manifold with boundary is a second-countable Hausdorff space $M$ in which every point has a neighborhood homeomorphic either to:

a) an open subset of $\R^n$ or

b) an open subset of $\H^n$.