Does "Topology" by Munkres ever mention filters?

I just started looking through Munkres, since my current Topology class is using it. However, it surprises me that I find no mention to filters (though he does have a short section about nets). A quick look at the index shows no mention of filters.

First, do you know if filters ever appear in the Munkres' "Topology" (2nd ed.)? E.g. as an exercise, without naming them, etc.

Second, it is my experience that filters are more natural to the study of topology than nets are. Do you know if there is a reason why Munkres never seems to mention filters, while he does have a set of exercises for nets? I.e. Is there a school of thought among topologists that prefers nets over filters?

Thanks!

Rita the dog2010-09-04T17:53:02Z

Favorite Answer

Just a comment because I don't know the answer to your question.

Paragraph (3) under Proofs of Tychonoff's theorem, here: http://en.wikipedia.org/wiki/Tychonoff%27s_theorem suggests to me that maybe Munkres (for whatever reasons) is deliberately trying to avoid filters.

MathNerd2010-09-07T20:55:23Z

I'm not 100% sure, but I used Munkres for two semesters of Topology and I never saw any mentioning of filters. We didn't cover the whole book though, so I suppose it's possible, but I don't believe Munkres mentions them. No idea why though.

Anonymous2016-04-13T03:17:31Z

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