A set that is a smooth embedded two-dimensional manifold except for a subset that consists of smooth embedded curves, except for a set of isolated points.
Stratified Manifold
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References
Morgan, F. "What is a Surface?" Amer. Math. Monthly 103, 369-376, 1996.Referenced on Wolfram|Alpha
Stratified ManifoldCite this as:
Weisstein, Eric W. "Stratified Manifold." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/StratifiedManifold.html