Do we have any information about definition of topology . Definition is not intuitive for me .Please share information about definition of topology .

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    $\begingroup$ Hi, welcome to hsm. Please see Wikipedia entry on the subject and try to ask the question more specifically if it does not have what you are looking for. en.wikipedia.org/wiki/Topology#History $\endgroup$ – Conifold Sep 8 '15 at 20:53
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    $\begingroup$ While the historical aspects of the definition of a topology are on-topic here, we aren't really the place to go for pedagogical insight. Math SE or Math Educators SE would seem to be better fits for such questions. If you really want the historical perspective, we can provide it, but that isn't apparent to me as you've written your question right now (and your question right now is rather broad). $\endgroup$ – Logan M Sep 9 '15 at 2:29
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    $\begingroup$ Why is a topology made up of 'open' sets? $\endgroup$ – user5402 Sep 11 '15 at 3:19

I suppose you are asking for the definition of topology as a mathematical term, not about the name of the part of mathematics.

The modern definition of topology is a product of long development. Originally open and closed sets were defined through accumulation points (Cantor). This is very intuitive. The basic notion was the notion of limit. Later, the operation of closure was introduced, described by axioms and a set was called closed if it coincides with its closure. This approach is used in the comprehensive book by Kuratowski, "Topology" written in the late 1930-s. Later it was found more convenient to define topology by simple axioms of open sets. Because of the Bourbaki influence this approach became standard.

Modern definition indeed looks very abstract to a beginner, but it has certain advantages. A good book which can be recommended as an introduction to topology is Chinn and Steenrod, First concepts of topology.

I learned these first notions from this book as a freshman undergraduate.

After that you can read some undergraduate textbook on topology, like Kelley, General topology, or some more modern undergraduate book.

Remark. For most questions studied in the undergraduate curriculum, the general definition of topology is not needed. So it is reasonable to familiarize yourself first with the special case of metric spaces (instead of the general case of topological spaces). metric spaces are explained in any good (rigorous) calculus textbook, in the beginning chapters. In metric spaces everything is defined in terms of the distance, a very intuitive notion.


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