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
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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.
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.
Funny, Funny stuff, or at least it was 2 years ago. Honestly I've seen this query MANY times since then. Where does the Bible mention Cars? I am a Christian, one of Jehovah's Witnesses. If a person looks for Direct words, quotes, phrases, etc. to allow/disallow things they will often, though not always, be rather disappointed. That said, being Humans, we have, some more than others, intellect and reasoning ability. Applying Bible PRINCIPLES is ever important, especially when Many terms now used weren't even part of the human lexicon centuries ago. As for studying, the Bible makes Many references to gathering together to study, both God's word directly, and to study/learn how to be better people, in general, and especially as Christians and Ministers. EdiT Nice one FA. I don't see the terms "Christmas Present", or "Halloween Costume" in the Bible either. EDiT again "If these hypocrites had any integrity they would leave their false religion." What a *achem* loving response. I love it when a total stranger, who, clearly, has issues in their own life, decides I have no integrity. It just encourages me even more that I must be on to something, if empty insults is the BEST the person can throw at me/my beliefs. EdiT again As FA mentioned, Field Service wasn't in the Bible, nor was Easter Bunny:D Nor was, for that matter Playboy Magazine, yet I imagine MOST Christian men are able to figure out whether or not we should be "reading" this periodical, on the other end the terms "Gas Station", Thermostat, or Computer, but, once again, I'd imagine Most people can decide whether or not, They as Christians should use these things. For that matter Necktie isn't in the Bible, but most guys, especially Christians it seems, where them.