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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
Krishnakant posted an Question
December 25, 2019 • 06:47 am
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15 points
15 points
- IIT JAM
- Mathematics (MA)
I want to understand compactness
1 Answer(s)
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Eduncle![best-answer]()
Hi Krishnakant,
Greetings!
Here is the solution of your query -
Compactness, property of some topological spaces (a generalization of Euclidean space) that has its main use in the study of functions defined on such spaces. An open covering of a space (or set) is a collection of open sets that covers the space; i.e., each point of the space is in some member of the collection. A space is defined as being compact if from each such collection of open sets, a finite number of these sets can be chosen that also cover the space.
The Formulation of this topological concept of compactness was motivated by the Heine-Borel theorem for Euclidean space, which states that compactness of a set is equivalent to the set’s being closed and bounded.
Thank you.