I'm self studying topology and so I don't have much direction, however I found this wonderful little pdf called topology without tears.(adsbygoogle = window.adsbygoogle || []).push({});

So to get to the meat of the question, given that [tex]\tau[/tex] is a topology on the setXgiving ([tex]\tau[/tex],X), the members of [tex]\tau[/tex] are called open sets. Up to that point I feel ok, but then the pdf goes to say that the compliment of those members are closed, and so I am guessing that is compliment of that set in reference to X.

So of X is a set of {1,2,3,4,5} and [tex]\tau[/tex] has a particular member that is {1} that the compliment of that would be {2,3,4,5}. And so up to here, hopefully I am understanding the material.

What really gets me is when you start getting sets on your topology which are to be closed, neither open or closed, or even clopen.

Why would you describe a topology to closed rather than open? Isn't being closed suppose to be relative to the members that you have in [tex]\tau[/tex] and the subsets of X which are considered open?

How can a topology be neither open nor closed, I don't get it.

I'm lost, thank you. For your help.

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# Topology Open and Closed Sets

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