# Cone space

From Topospaces

This article describes a construct that involves some variant of taking a product of a topological space with the unit interval and then making some identifications, typically at the endpoints, based on some specific maps.

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## Definition

Given a topological space , the **cone space** of , denoted as , is defined as the quotient of (where is the closed unit interval and we use the product topology) by the equivalence relation:

Here, refers to the closed unit interval .

Refer:

- Cone space functor to see the properties of the cone space functor
- Cone-realizable space to see the property of a topological space being realizable as the cone space over some space