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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- IIT JAM
- Mathematics (MA)
Mathematics (point set topolog 9. compactnesss i) open cover of a set definition: let s cr and c {a| i e l}, r be the group of oden set in r. then c is called t
somebody please explain this with details and proper examples.
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Deepak singh 1 Best Answer
Open cover - is a collection of open sets of a topological space whose union contains a given subset. For example, - 1. an open cover of the real line, with respect to the euclidean topology , is the set of all open intervals (-n,n) where n €N 2. The set of all intervals (1/n,1) , where n€N\{0} , is an open cover of the open interval (0,1). Finite Subcover - if above collection of open sets have a finite subset whose union also covers giver set . then this set is called finite subcover. Compact - if every open cover has a finite subcover, (or equivalently that every open cover has a finite refinement); for more understanding go through given link https://youtu.be/Y3iy2Gkp7VY