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Given a topological vector space X and a neighborhood V of 0 in X, the polar K=K(V) of V is defined to be the set K(V)={Lambda in X^*:|Lambdax|<=1 for every x in V} and where ...

A topological space, also called an abstract topological space, is a set X together with a collection of open subsets T that satisfies the four conditions: 1. The empty set ...

A lens space L(p,q) is the 3-manifold obtained by gluing the boundaries of two solid tori together such that the meridian of the first goes to a (p,q)-curve on the second, ...

The triangle space T is the set of triples (a,b,c) of real numbers that are side lengths of a (Euclidean) triangle, i.e., T={(a,b,c):0<a<b+c,0<b<c+a,0<c<a+b} (Kimberling ...

Let X be a connected topological space. Then X is unicoherent provided that for any closed connected subsets A and B of X, if X=A union B, then A intersection B is connected. ...

Riemann's moduli space R_p is the space of analytic equivalence classes of Riemann surfaces of fixed genus p.

The underlying set of the fundamental group of X is the set of based homotopy classes from the circle to X, denoted [S^1,X]. For general spaces X and Y, there is no natural ...

According to many authors (e.g., Kelley 1955, p. 112; Joshi 1983, p. 162; Willard 1970, p. 99) a normal space is a topological space in which for any two disjoint closed sets ...

A topological space that is not connected, i.e., which can be decomposed as the disjoint union of two nonempty open subsets. Equivalently, it can be characterized as a space ...

A real vector space is a vector space whose field of scalars is the field of reals. A linear transformation between real vector spaces is given by a matrix with real entries ...