Topological Manifold
A Topological Space 
satisfying some separability (i.e., it is a Hausdorff Space) and countability(i.e., it is a Paracompact Space) conditions such that every point 
has a Neighborhood homeomorphicto an Open Set in 
for some 
. Every Smooth Manifold is a topological manifold, but notnecessarily vice versa. The first nonsmooth topological manifold occurs in 4-D.
Nonparacompact manifolds are of little use in mathematics, but non-Hausdorff manifolds do occasionally arise in research(Hawking and Ellis 1975). For manifolds, Hausdorff and second countable are equivalent to Hausdorff and paracompact, andboth are equivalent to the manifold being embeddable in some large-dimensional Euclidean space.
See also Hausdorff Space, Manifold, Paracompact Space, Smooth Manifold, Topological Space
References
Hawking, S. W. and Ellis, G. F. R. The Large Scale Structure of Space-Time. New York: Cambridge University Press, 1975.
- Bra
- Brachistochrone Problem
- Bracket
- Bracketing
- Bracket Polynomial
- Bracket Product
- Bradley's Theorem
- Brahmagupta Identity
- Brahmagupta Matrix
- Brahmagupta Polynomial
- Brahmagupta's Formula
- Brahmagupta's Problem
- Braid
- Braid Group
- Braid Index
- Braid Word
- Braikenridge-Maclaurin Construction
- Branch
- Branch Cut
- Branch Line
- Branch Point
- Brauer Chain
- Brauer Group
- Brauer Number
- Brauer-Severi Variety