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Having decided on a physics/math double major next year, I decided to get a head start this summer.

After tackling some classical mechanics, my next target is topology.

My problem is the following: I have been informed that there are two approaches to the subject, one involving filters and the other one involving nets (note that these terms are directly translated from Dutch, if other terms are used in English I apologize).

I've been told my topology professor for next year favours the filters. I have found some textbooks online, but a friend has told me they use the net approach.

My question is this: could somebody explain to me the difference between the two approaches, without going into too much detail. Also, it would be greatly appreciated if someone could point me in the direction of any online textbooks that deal with the filters approach.

Thanks in advance,

-Dimi