Topological Manifold - Manifolds With Boundary

Manifolds With Boundary

A slightly more general concept is sometimes useful. A topological manifold with boundary is a Hausdorff space in which every point has a neighborhood homeomorphic to an open subset of Euclidean half-space (for a fixed n):

The terminology is somewhat confusing: every topological manifold is a topological manifold with boundary, but not vice-versa.

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Famous quotes containing the word boundary:

    “The boundary line between self and external world bears no relation to reality; the distinction between ego and world is made by spitting out part of the inside, and swallowing in part of the outside.”
    —Norman O. Brown (b. 1913)