This question is not as much a research question as it is a poll or survey.
Dear Matt Insall ,
I don't use nonstandard topology and not intend to use it at all
for many reasons. Here some of them:
(1) If (X, T) is a metric space and (X, F) is another topological space
that is homeomorphic to (X, T). If (P) is any proposition in (X, T)
it is silly to talk about new results analog to (P) in (X, F).
Similar issue for the standard and nonstandard topologies,
even they are related to different assumptions and different axioms!!
(2) I read an article, where the author writes 12 pages to show very trivial properties of the nonstandard topology over the reals R.
(3) The common trend is to modify and simplify the topological concepts for the students and researchers, not to create more useless complications.
(4) The lack of practical applications.
Conclusion: I think the idea of nonstandard topology models is a (fake)
reproduction of the great efforts of others to find a new (area )
where endlessly well-known results reproduced in a deformed way.
Dear Matt,
I hope you will consider my opinion as a point of view, not more. May many others have different thoughts; at least you are one of them.
Best regards
Dear Professor Kaddoura,
Thank you for your reply.
You seem to have not included any topology research on your researchgate site. Do you have any topology papers that you can share?
Best Regards,
Dr. Matt Insall
Dear Matt Insall
I hope you find the following articles are interesting.
Best regards
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