Talk:Cone (topology)

This article makes the standard mistake about cones; it assumes that the cone is defined via the quotient topology and then it pretends that the homotopy


 * ht(x,s) = (x, (1&minus;t)s).

is obviously continuous. Thus cones are obviously contractible to their apex. I don't know a treatment that makes this transparently obvious... Here is one discussion:. Sam nead (talk) 15:58, 28 December 2017 (UTC)

Notation "lim"
Is the notation $$CX = \varinjlim \bigl( (X \times [0,1]) \hookleftarrow (X\times \{0\}) \xrightarrow{p} v\bigr)$$ meant to suggest that the cone is the pushout of the indicated span? If so, please write it explicitly. 164.15.244.37 (talk) 07:43, 25 February 2022 (UTC)