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.
- Gaullist Cross
- Gauss-Bodenmiller Theorem
- Gauss-Bolyai-Lobachevsky Space
- Gauss-Bonnet Formula
- Gauss-Bonnet Theorem
- Gauss Equations
- Gaussian Approximation Algorithm
- Gaussian Bivariate Distribution
- Gaussian Brackets
- Gaussian Coefficient
- Gaussian Coordinate System
- Gaussian Curvature
- Gaussian Differential Equation
- Gaussian Distribution
- Gaussian Distribution Linear Combination of Variates
- Gaussian Elimination
- Gaussian Function
- Gaussian Hypergeometric Series
- Gaussian Integer
- Gaussian Integral
- Gaussian Integral (Linking Number)
- Gaussian Joint Variable Theorem
- Gaussian Mountain Range
- Gaussian Multivariate Distribution
- Gaussian Polynomial