TOPICS
Search

Manifold with Boundary


An n-dimensional manifold with boundary is a Hausdorff, second countable topological space in which every point has a neighborhood homeomorphic to an open subset of the closed half-space

 H^n={(x_1,...,x_n) in R^n:x_n>=0}.

Points represented with x_n=0 form the boundary, which is an (n-1)-dimensional manifold without boundary. The closed ball is a manifold with boundary whose boundary is a sphere.


See also

Boundary, Manifold, Open Manifold

Explore with Wolfram|Alpha

References

Lee, J. M. Introduction to Topological Manifolds, 2nd ed. New York: Springer, 2011.

Cite this as:

Weisstein, Eric W. "Manifold with Boundary." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ManifoldwithBoundary.html

Subject classifications