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Homotopy extension property of cone

Properties1
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Problem

Show that the cone over

has the homotopy extension property.

Quote

Not all inclusions are created equal.
1

Homotopy extension property

Let be a topological space and let . We say has the homotopy extension property if for a homotopy and a map such that there exists a homotopy

that starts from and extends , that is,

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Footnotes

  1. math.jhu.edu/~jmb/note/hep.pdf ↩

  2. algebraic topology - Homotopy Extension Property of mapping cone - Mathematics Stack Exchange ↩

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