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The term "homology group" usually means a singular homology group, which is an Abelian group which partially counts the number of holes in a topological space. In particular, ...

Let K be a finite complex, let h:|K|->|K| be a continuous map. If Lambda(h)!=0, then h has a fixed point.

If F is a sigma-algebra and A is a subset of X, then A is called measurable if A is a member of F. X need not have, a priori, a topological structure. Even if it does, there ...

A distance g on a set that fulfils the same properties as a metric except relaxes the definition to allow the distance between two different points to be zero. An example of ...

That portion of mathematics dealing with functions of real variables. While this includes some portions of topology, it is most commonly used to distinguish that portion of ...

A topological partial algebra is a pair (A,tau), where A=(A,(f_i^A)_(i in I)) is a partial algebra and each of the operations f_i^A is continuous in the product topology. ...

A graph G is transitive if any three vertices (x,y,z) such that edges (x,y),(y,z) in G imply (x,z) in G. Unlabeled transitive digraphs are called digraph topologies.

The term "twisted sphere" is used to mean either a projective plane (Henle 1994, p. 110) or the corkscrew surface obtained by extending a sphere along a diameter and then ...

Complex Analysis

Differential Geometry