Extension Topology

In topology, a branch of mathematics, an extension topology is a topology placed on the disjoint union of a topological space and another set.

There are various types of extension topology, described in the sections below.

Read more about Extension Topology:  Extension Topology, Open Extension Topology, Closed Extension Topology

Other articles related to "extension topology, topology":

Closed Extension Topology
... Consider in X ∪ P the topology whose closed sets are of the form X ∪ Q, where Q is a subset of P, or B, where B is a closed set of X ... For this reason this topology is called the closed extension topology of X plus P, with which one extends to X ∪ P the closed sets of X ... Note that the subspace topology of X as a subset of X ∪ P is the original topology of X, while the subspace topology of P as a subset of X ∪ P is the discrete topology ...

Famous quotes containing the word extension:

    We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because he has neither extension nor limits.
    Blaise Pascal (1623–1662)