union of two compact subset of metric space is compact|compactness|UPSCoptional |B.Sc.3rdyr|L37

Описание: topic cover
union of two compact subset of metric space is compact.

topic cover in lecture 36
   • every closed subset of compact metric spac...  
compact space
every closed subset of compact metric space is compact .

topic cover in lecture 35
   • function is continuous iff image of closur...  
f is continuous iff image of closure of A is subset of closure of image of A, A is subset of X

topic cover in 34
   • Inverse image of CLOSED is Closed iff func...  
inverse image of open is open iff function is continuous

topic cover in lecture 33
   • Inverse image of open is open iff function...  
inverse image of open is open iff function is continuous

topic cover in lecture 32
   • Density Theo|between every two different r...  
Density Theorem
between every two different real no. there exist atleast one rational no.

topic cover in lecture 31
   • Archimedean Property in real|proof|B.Sc.3r...  
Archimedean Property in real, with proof

topic cover in lecture 30
   • Sup(S+T) = Sup S + Sup T |proof|  |propert...  
property of supremum
sup (S+T) = sup S + sup T

topic cover in lecture 29
   • |x+y| less than equal |x|+|y|  |proof|  ||...  
properties of mode
|x+y| less than equal to |x|+|y|
||x|-|y|| less than equal to |x-y|

topic cover in lecture 28
   • real no. as complete ordered field| √2 is ...  
real no. as complete ordered field
√2 is not a rational no.

topic cover in lecture 27
   • Metric space (R,d) is complet|d ususal met...  
completeness in R
every (R,d) metric space is complete where d is usual metric space

topic cover in lecture 26
   • Complete metric space|in complete metric, ...  
complete metric space
if (X,d) is complete metric space and Y is a subspace of X then if Y is complete iff Y is closed.

topic cover in lecture 25
   • Every CAUCHY sequence in a metric space is...  
every cauchy sequence in a metric space is bounded.
E is a subset of metric space (X,d). E is bounded iff diameter of E is finite real number.

topic cover in lecture 24
   • Every convergent sequence in a metric spac...  
cauchy sequence
convergent sequence
Every convergent sequence in a metric space is cauchy. but its converse is not true.

topic cover in lecture 23
   • Every convergent sequence in a metric spac...  
definition : closure set
interior of set
bounded set
Every convergent sequence in a metric space is bounded.

Topic cover in lecture 22
   • set is Closed if it contain its Derived se...  
in a metric space, union of finite number of closed set is closed.
in a metric space, a set is closed if and only if it contains its set of limit point.

topic cover in lecture 21
   • closed SPHERE is a closed SET|intersection...  
in metric space, every closed sphere is a closed set.
in metric space, the intersection of an arbitrary collection of closed set is closed.

topic cover in lecture 20
   • Intersection of finite no of open set is o...  
In metric space, the intersection of a finite number of open sets is open.

topic cover in lecture 19
   • In Metric Space|Open sphere are open set|B...  
In a metric space, every open sphere is an open set.

topic cover in lecture 18
   • Part 2|Metric Space|practice ques.|B.Sc 3r...  
some more examples : to solve metric

topic cover in lecture 17
   • Metric Space|practice ques.|B.Sc 3rd year|...  
Metric space
question to check mapping is metric

topic cover in lecture 16
   • Fourier series of function of period 2pie|...  
Fourier Series of function with period 2 pie

Topic cover in lecture 15
   • Abel's|Drichlete|Test for convergence of 2...  
Test for the convergence of Beta function
Abel's test for 2nd kind of improper integral(prac. que. )
Drichlete test for 2nd kind of improper integral(prac. que.)

topic cover in lecture 14
   • Test for convergence of 2nd improper integ...  
Test for the convergence of 2nd kind of improper integral
Comparison test
Mue test

topic cover in lecture 13
   • Abel's|Drichlet|comparisionIMue test|Test ...  
test of convergence of first kind of improper integral
necessary and sufficient condition
comparison test
miu test
abel's test
drichlete test
absolute convergence
practice questions

topic cover in in lecture 12
   • Test for convergence of improper integral|...  


this lecture is beneficial for B.Sc. III yr students , students target UPSC optional, etc.
as it content proofs of imp ques. with complete understanding.

playlist:

lectures on real analysis part II (with proofs) beneficial for students target B.Sc, M.Sc., UPSC Optional.


lectures on REAL ANALYSIS (target NET, JAM, GATE, SET, NBHM, TIFFER.... etc.
   • Real analysis (CSIR NET,JAM,GATE,PhD,MSC e...  

CSIR NET 2020maths, solved question paper:    • CSIR NET  2020maths, solved question paper  

lectures on Group theory:    • Lectures on group theory  

Lectures on Discrete Mathematics:    • Lectures on Discrete Mathematics  



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