Math, asked by neelampatel06026, 8 months ago

4. (a)
कैन्टर का सर्वनिष्ठ प्रमेय लिखिए एवं सिद्ध कीजिए।
State and prove Cantor's intersection theorem.​

Answers

Answered by debasisnandy01
6

Answer:

Cantor's intersection theorem refers to two closely related theorems in general topology and real analysis, named after Georg Cantor, about intersections of decreasing nested sequences of non-empty compact sets.

Answered by greeshmakachirayil
0

Answer:

The Cantor set is defined as the  crossroad of a  dwindling nested sequence of sets, each of which is defined as the union of a finite number of unrestricted intervals; hence, each of these sets isnon-empty, unrestricted, and bounded. This  description is a straight forward corollary of the theorem.  

In order to demonstrate this, we will first demonstrate that| A|| P( A)| and  also that( 2)| A| = | P( A)|. This is original to the  expression of the  handed theorem's strict  lower than clause.( 1)| A| ≤| P( A)| Now, to demonstrate this, all we've to do is  produce a bijection between A and a subset ofP.( A). also we'll know that group, which can not be bigger than P, has the same size asA.( A).  Consider the collection of all A's single- element subsets, E =  x x A. Since it's composed of several subsets of A, it's apparent that E P( A). It's also a  licit subset because we're  apprehensive that it's devoidof.Thus its is proofed.

To know more about intersection  

https://brainly.in/question/45053927

To know more about  Cantor's  theorem

https://brainly.in/question/54319993

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