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

h_t(x,s) = (x, (1−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: ^[1]. Sam nead (talk) 15:58, 28 December 2017 (UTC)[reply]

Notation "lim"[edit]

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)[reply]

^ https://math.stackexchange.com/questions/189978/the-cone-is-contractible

[1] ttps://math.stackexchange.com/questions/189978/the-cone-is-contractible

[1]