Real Analysis | Limit Point | Derived Set, Closed Set & Closure Of Set Definition & Examples
Real Analysis | Limit Point | Derived Set, Closed Set & Closure Of Set Definition & Examples #viral
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This video lecture of Real Analysis | Limit Point | Derived Set & Closure Of Set Definition & Examples | Problems & Concepts by GP Sir will help Engineering and Basic Science students to understand the following topic of Mathematics:
1. What is the Limit Point Of Set in Real Analysis?
2. Definition and Examples Of Derived Set, Closure Of Set.
3. What is the Concept & Examples of Closed Set By Derived Set.
4. This helpful For CSIR NET, IIT-JAM, GATE Exams.
5. This is Part Of Real Analysis.
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This Concept is very important in Engineering & Basic Science Students. This video is very useful for B.Sc./B.Tech & M.Sc./M.Tech. students also preparing for NET, GATE, and IIT-JAM Aspirants.
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Bolzano weierstrass theorem : Every infinite bounded subset of R has a limit point.
Definition of Neighbourhood of a point
Definition of Open set
infinite intersection of open sets need not to be open
Union of two NBDS is NBD
Intersection of NBDS is NBD
Superset of a NBD is also a NBD
Every Open interval (a,b) is neighbourhood of each of its points.
Closed interval is neighbourhood of each point except end points.
real numbers is NBD of each real number
Rational numbers set is not the neighbourhood of any of its points.
Metric space | Distance Function | Example
Metric space : Definition and Axioms
Real Analysis : Introduction and Intervals
Union of countable sets is countable
Finite,infinite,equivalent,denumerable,countable sets
Infinite subset of countable set is countable
Field,Ordered Field,complete Ordered Field
Set of Integers is Countable
Supremum and infimum
Set is countably infinite iff it can be written in the form distinct elements
Continuum Hypothesis
Cartesian product of two countable sets is Countable
Set of Rational numbers is Countable
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