It is well-known that there are two different ways to generalize the theory of convergence of sequences to arbitrary topological spaces: nets and filters. They are of course essentially equivalent, but each has its own minor advantages for pedagogy and intuition. Seemingly less well-known is th...
I hope that we both have in mind the same notion of convergence of a sequence along an ultrafilter on $\mathbb N$.
I know that you asked for a reference. Instead of giving a reference, I have copied a part of my LaTeXed notes I made for myself sometimes ago instead. In these notes I work with fu...
I hope that we both have in mind the same notion of convergence of a sequence along an ultrafilter on $\mathbb N$.
I know that you asked for a reference. Instead of giving a reference, I have copied a part of my LaTeXed notes I made for myself sometimes ago instead. In these notes I work with fu...
@EricWofsey I see that my notes on the topic have been mentioned. I am not sure whether I can add something which is not already mentioned in these notes or in the posts linked here. (I have recently posted a comment to Brian M. Scott's answer with some additional links.) In any case, feel free to drop me a line in chat or via email if I can be of more assistance. — Martin Sleziak1 min ago
Thanks for mentioning my notes (still unfinished...). I will add link to this answer and to this conversation in chat. I am posting them here for two reasons: 1) Some other references and links to related posts can be found there. 2) Also the fact that this generalizes both limits of filters and limits of nets is mentioned there. — Martin Sleziak6 hours ago
@Martin: You’re very welcome. I’ll add both links to my answer to make them a little more visible. — Brian M. Scott5 hours ago
@MartinSleziak: Thank you for sharing those links! In particular, I might suggest that you copy some of the references from that chat as an additional answer to this question. — Eric Wofsey5 hours ago
Per the OP's request from this comment I am posting some stuff about references I am aware of. Those references are mentioned in my (unfinished) notes on this topic and also in this answer and this conversation in chat. The purpose of reposting them here is that the linked resources have somewhat...
@EricWofsey Just in case you will peek into this room, let me add a short comment.
I ended up writing rather long post. (Longer than I expected.) And I am not sure to which extent it adds some value to the stuff which was already mentioned.
But maybe you (or somebody else reading that post) will find some of the stuff posted there interesting/useful.
I should also add that I wrote those notes mainly for my needs. (And also for some colleagues attending the same seminar.) I have no problem admitting that they are still incomplete and they could be better organized.
