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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
Divya Sree Reddy posted an Question
February 01, 2022 • 23:48 pm
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30 points
30 points
- CSIR NET
- Mathematical Sciences
Ra - in real analysis what is a connected, open , bounded, compact sets. please explain briefly.
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Anonymous User
A set S of real numbers is called bounded from above if there exists some real number k (not necessarily in S) such that k ≥ s for all s in S. ... A set S is bounded if it has both upper and lower bounds. Therefore, a set of real numbers is bounded if it is contained in a finite interval.
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Anonymous User
A set S of real numbers is called compact if every sequence in S has a subsequence that converges to an element again contained in S
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Anonymous User
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A connected set is a set that cannot be partitioned into two nonempty subsets which are open in the relative topology induced on the set. Equivalently, it is a set which cannot be partitioned into two nonempty subsets such that each subset has no points in common with the set closure of the other.
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Anonymous User
The distance between real numbers x and y is |x - y|. ... An open subset of R is a subset E of R such that for every x in E there exists ϵ > 0 such that Bϵ(x) is contained in E. For example, the open interval (2,5) is an open set. Any open interval is an open set.