Timeline for Mapping space from a quotient space

Current License: CC BY-SA 4.0

15 events

when toggle format	what		by	license	comment
S Feb 5, 2019 at 7:37	history	suggested	Victor	CC BY-SA 4.0	Removed "or $Y=\{0,1\}$" in the last sentence as it doesn't make a counterexample to the first question.
Feb 5, 2019 at 5:20	review	Suggested edits
S Feb 5, 2019 at 7:37
Jul 9, 2017 at 18:49	history	edited	Taras Banakh	CC BY-SA 3.0	edited body
Jul 9, 2017 at 16:29	comment	added	Wlod AA		Taras, your example is very nice--purely conceptual, very clean.
Jul 9, 2017 at 16:17	comment	added	მამუკა ჯიბლაძე		The counterexample would produce a situation when the canonical injection$$\operatorname{Cont}([0,1],Y)\to\operatorname{Cont}(\alpha N,Y)^{\operatorname{Cont}(\alpha N,[0,1])}$$is not a homeomorphic embedding. My problem is that I have no idea what topology sits on $\operatorname{Cont}([0,1],Y)$. For a general $Y$ there is no single decent topology there I believe.
Jul 9, 2017 at 16:01	history	edited	Taras Banakh	CC BY-SA 3.0	deleted 1 character in body
Jul 9, 2017 at 15:56	vote	accept	Victor
Jul 9, 2017 at 15:53	history	edited	Taras Banakh	CC BY-SA 3.0	added 4 characters in body
Jul 9, 2017 at 15:51	comment	added	Taras Banakh		@Wlod-AA My $X$ is the topological sum of all convergent sequences in $[0,1]$, so is not discrete. The map $q$ is quotient because for any non-closed subset $F\subset [0,1]$ there exists a convergent sequence $S\subset [0,1]$ such that $S\cap F$ is not closed in $S$ and then $q^{-1}(F)$ is not closed in $X$.
Jul 9, 2017 at 15:47	history	edited	Taras Banakh	CC BY-SA 3.0	added 4 characters in body
Jul 9, 2017 at 15:16	comment	added	Wlod AA		Would you go into more details, please?
Jul 9, 2017 at 15:12	comment	added	Wlod AA		Isn't your $X$ discrete?
Jul 9, 2017 at 15:09	comment	added	Wlod AA		Typo? Do you mean $\dots\subset [0;1]\times\mathcal S\ $ ?
Jul 9, 2017 at 11:27	history	edited	Taras Banakh	CC BY-SA 3.0	added 11 characters in body
Jul 9, 2017 at 8:35	history	answered	Taras Banakh	CC BY-SA 3.0