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A space X is locally pathwise-connected if for every neighborhood around every point in X, there is a smaller, pathwise-connected neighborhood.

Let c=(c_1,...,c_n) be a point in C^n, then the open polydisk is defined by S={z:|z_j-c_j|<|z_j^0-c_j|} for j=1, ..., n.

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

A sum which includes both the Jacobi triple product and the q-binomial theorem as special cases. Ramanujan's sum is ...

In nonstandard analysis, the transfer principle is the technical form of the following intuitive idea: "Anything provable about a given superstructure V by passing to a ...

The point at which the three lines connecting the polygon vertices of perspective triangles (from a point) concur, sometimes also called the homology center, pole, or, in ...

Given a triangle, extend two sides in the direction opposite their common vertex. The circle tangent to these two lines and to the other side of the triangle is called an ...

A topology that is "potentially" a metric topology, in the sense that one can define a suitable metric that induces it. The word "potentially" here means that although the ...

Noncommutative topology is a recent program having important and deep applications in several branches of mathematics and mathematical physics. Because every commutative ...

Let X be a topological vector space and for an arbitrary point x in X, denote by N_(x) the collection of all neighborhoods of x in X. A local base at x is any set B subset ...