Cone space

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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 X, the cone space of X, denoted as CX, is defined as the quotient of X \times I (where I is the closed unit interval [0,1] and we use the product topology) by the equivalence relation:

(x_1,0) \sim (x_2,0) \forall x_1,x_2 \in X

Here, I refers to the closed unit interval [0,1].

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