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

... Consider in X ∪ P the

**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)

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