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A topological space X has a one-point compactification if and only if it is locally compact. To see a part of this, assume Y is compact, y in Y, X=Y\{y} and x in X. Let C be ...

A map which sends open sets to open sets.

In a topological space X, an open neighborhood of a point x is an open set containing x. A set containing an open neighborhood is simply called a neighborhood.

A nonsimply connected 3-manifold, also called a dodecahedral space.

The pseudo-tangent cone P_S(x) of a subset S subset R^n at a point x in S is the set P_S(x)=convK_S^_, where K_S is the contingent cone of S and where conv(A) is the smallest ...

The complex plane C with the origin removed, i.e., C-{0}. The punctured plane is sometimes denoted C^* (although this notation conflicts with that for the Riemann sphere C-*, ...

A set S with a single point P removed is called a punctured set, written S\{P}.

An outer measure mu on R^n is Borel regular if, for each set X subset R^n, there exists a Borel set B superset X such that mu(B)=mu(X). The d-dimensional Hausdorff outer ...

A Reinhardt domain with center c is a domain D in C^n such that whenever D contains z_0, the domain D also contains the closed polydisk.

In a complete metric space, a countable union of nowhere dense sets is said to be meager; the complement of such a set is a residual set.