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Martin Sleziak
Martin Sleziak
12:27 PM
1
Q: Reference for convergent nets as continuous functions from $D\cup\{\infty\}$

Martin SleziakIf we have any directed set $(D,\le)$ then we can add a point $\infty\notin D$ and then consider the topology on $C(D)=D\cup\{\infty\}$ such that all points of $D$ are isolated and the local base at $\infty$ consists of all "upper sets" $\langle d,\infty\rangle=\{\infty\}\cup\{d'\in D; d'\ge d\}$...

general-topology reference-request continuity nets
Do you know tha treatment of convergence in Preuss Topologische Räume I? It's even more general and IMO quite elegant. No mention of your $D$ though. For sequences we have one space to deal with and for nets a huge class of such spaces (characterised by being almost discrete, i.e. having exactly one non-isolated point). — Henno Brandsma 4 hours ago
I have some trouble which books is meant here.
The Wikipedia article Gerhard Preuß (Mathematiker) mentions Allgemeine Topologie and Foundations of Topology - An Approach to Convenient Topology - I have access to both these books.
But I did not find a book called "Topologische Räume". Google, Google Books, Google Scholar.
There is a book by Horst Herrlich called Topologie I: Topologische Räume. (However, I have only access to Topologie II: Uniforme Räume.)
@HennoBrandsma I wasn't sure which book you mean here. I did not find a book by G. Preuss with this title. (There is a book by H. Herrlich called Topologie I: Topologische Räume - but I do not have access to that one.) I left more details in chat. — Martin Sleziak 11 secs ago
 
Martin Sleziak
Martin Sleziak
1:03 PM
Yeah it’s Herrlich. I have it on my shelves; part 2 on Uniforme Räume too — Henno Brandsma 14 mins ago
Thanks for the response. I will try to find out whether I can get hold of it. — Martin Sleziak 52 secs ago
 
Martin Sleziak
Martin Sleziak
1:27 PM
Slovaks can probably read German pretty well (and Russian too). Handy in maths too. — Henno Brandsma 17 mins ago
 

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