Talk:General topology

message: I see such subsection (11.6), with only the link "Main article: Topology"; and I do not see anything like that in "Topology" article. What is meant by "Foundations of topology"? And more generally: separate foundations for each branch of mathematics? Or "federal" foundations of the whole mathematics? Boris Tsirelson (talk) 06:31, 6 February 2015 (UTC)
replies: text: When I rewrote the article, I used online lists of topics related to general topology. I wasn't sure what "foundations of topology" was either. Feel free to omit it.Brirush (talk) 12:32, 6 February 2015 (UTC)
replies: text:  Well, if so, I just did. Whoever knows whats'it, feel free to insert it. Boris Tsirelson (talk) 15:28, 6 February 2015 (UTC)
thread_title:  Foundations of topology 

message: Substituted at 02:08, 5 May 2016 (UTC)
thread_title: Assessment comment

message: There are at least two mistakes in this section: http://math.stackexchange.com/questions/2101750/continuous-functions-define-a-topology . I don't think I'm competent to clean this up, and I'm not sure if I understand the intention of the author.--76.169.116.244 (talk) 23:29, 17 January 2017 (UTC)
replies: text: Yes, thank you, I see the problem(s). Yes, the intention of the author is vague, since the class of all continuous functions into all topological spaces must satisfy some conditions, not specified here. (The same problem for the dual approach.) On the other hand, it is easy to see that this class determines uniquely the given topology. Indeed, given two topologies \tau_1, \tau_2 on S, we may consider all continuous functions S\to X_k for X_1 = (S,\tau_1), X_2 = (S,\tau_2) and check continuity of the identity maps f_1:S\to X_1, f_2:S\to X_2. Clearly, f_1 is continuous w.r.t. \tau_1, and f_2 is continuous w.r.t. \tau_2. Now, if \tau_1, \tau_2 have the same continuous functions, then also f_1 is continuous w.r.t. \tau_2, and f_2 is continuous w.r.t. \tau_1, which means \tau_1=\tau_2. Boris Tsirelson (talk) 07:49, 18 January 2017 (UTC)
replies: text: Apparently that section was copied from Continuous function to Point-set topology () which was later merged into General topology (). I.e., Continuous function#Defining topologies via continuous functions still contains very much the same text. Furthermore, a variant of that text first appeared at Continuous function (topology) which had then been merged into Continuous function (). Anyway, any mistake that is fixed at General topology#Defining topologies via continuous functions probably needs to be fixed at Continuous function#Defining topologies via continuous functions, too.—Tea2min (talk) 09:35, 18 January 2017 (UTC)
replies: text: Wow... Then, I'll just do the same fix there. Thanks. Boris Tsirelson (talk) 09:58, 18 January 2017 (UTC)

text: In fact, the author was User:Jakob.scholbach, Aug 2011. Boris Tsirelson (talk) 10:12, 18 January 2017 (UTC)
thread_title: Errors in the section "Defining topologies via continuous functions"

message: I propose to add a reference to Algebraic_General_Topology._Volume_1 because it is a notable, authoritative work important in the context of general topology and relevant for the content of this article as a natural generalization of general topology.
Probably we should also create a page about algebraic general topology as a math branch (not just as about a book).
Huh?
--VictorPorton (talk) 22:40, 1 October 2019 (UTC)
replies: text: As you can see on your own talk page, the article Algebraic_General_Topology._Volume_1 has already been deleted twice.—Anita5192 (talk) 01:04, 2 October 2019 (UTC)
thread_title:  Proposed reference to algebraic general topology