#in

topic cover
In a usual metric space (R,U), a subset A of R is connected iff it is an interval.
topic cover in lecture 41
• #arbitrary union of no...
separated set
disconnected set
connected set
In a metric space, a family of connected set is such that their intersection is non empty then their union is connected.
topic cover in lecture 40
• #Every compact subset ...
every compact subset of a metric space is closed and bonded.
topic cover in lecture 39
• Every compact metric s...
Every compact metric space has bolzano weierstrass property
topic cover in lecture 38
• A metric space is sequ...
sequentially compact
Bolzano Weierstrass Property
A metric space is sequentially compact iff it has bolzano weierstrass prperty.
topic cover in lecture 37
• union of two compact s...
union of two compact subset of metric space is compact.
topic cover in lecture 36
• every closed subset of...
compact space
every closed subset of compact metric space is compact .
topic cover in lecture 35
• function is continuous...
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 CLOSE...
inverse image of open is open iff function is continuous
topic cover in lecture 33
• Inverse image of open ...
inverse image of open is open iff function is continuous
topic cover in lecture 32
• Density Theo|between e...
Density Theorem
between every two different real no. there exist atleast one rational no.
topic cover in lecture 31
• Archimedean Property i...
Archimedean Property in real, with proof
topic cover in lecture 30
• Sup(S+T) = Sup S + Sup...
property of supremum
sup (S+T) = sup S + sup T
topic cover in lecture 29
• |x+y| less than equal ...
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 o...
real no. as complete ordered field
√2 is not a rational no.
topic cover in lecture 27
• Metric space (R,d) is ...
completeness in R
every (R,d) metric space is complete where d is usual metric space
topic cover in lecture 26
• Complete metric space|...
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 ...
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 seque...
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 seque...
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 co...
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 clo...
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...
In metric space, the intersection of a finite number of open sets is open.
topic cover in lecture 19
• In Metric Space|Open s...
In a metric space, every open sphere is an open set.
topic cover in lecture 18
• Part 2|Metric Space|pr...
some more examples : to solve metric
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 NE...
CSIR NET 2020maths, solved question paper: • CSIR NET 2020maths, s...
lectures on Group theory: • Lectures on group theory
Lectures on Discrete Mathematics: • Lectures on Discrete M...
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[@103anushkasingh3]

Best explanation tqsm maam❤

[@amalsing6176]

Thank You Ma'am

[@jsmathzone3286]

Thanks mam. Keep doing more videos..❤from Kerala

[@shubhamsahu2531]

Thankyou mam ... Beutiful voice with beautiful explanation .... Honestly very helpful

[@divitasharma]

My pleasure 😊

[@hemasahu1593]

Thank you mam 🥰🙏 very nice explanation 😊

[@divitasharma]

Most welcome 😊

[@Harish-Dhar-Deewan]

Nice explain mam pura smj aa gya book ka to kuch v smj ni aa rha tha.....mam csir net ki study k liye v kuch guide kijiye

[@vdha3adiga]

Tq mam