f is continuous iff f inverse C is closed set in X for every closed set C in Y | Real Analysis

Показать описание

f from x to y is continous iff f inverse C is Closed set in X for a Closed set C in Y | Theorem | Continuity of function | Limit and Continuity | Real analysis | OMG Maths | Classes By Cheena Banga. | #omgmaths

Pdf link:
****Limit and Continuity****
****Real Analysis playlist****

useful for Msc | BSC | NET | NBHM | LPU | DU | IIT JAM | TIFR

Other topics covered in playlist:
Limit Inferior and limit superior definition and theorems
Cauchy Sequence in Compact Metric Space is Convergent
nth tail of sequence
Tail of a sequence
P Series Test for convergence of series
Limit Comparison Test for Convergence
Cantor Intersection Theorem
E is a subset of metric space X then Diameter of closure of E is equal to Diameter of E
Cauchy First theorem on limits
Bolzano Weierstrass Theorem
Every bounded sequence has a convergent sub sequence
Every Cauchy sequence is a Bounded sequence
Every convergent Sequence is cauchy sequence
Cauchy Sequence
Cauchy Sequence Definition
Cauchy Sequence theorems
Sub sequence of a sequence
Algebraic Properties of Limits
Algebra of limit of sequence
Properties of limit
limit laws of sequence
sandwich theorem
squeeze theorem
Sequence and series
real sequence
range of sequence
constant sequence
uniqueness theorem
Sequences in metric space
limit of sequence
Convergent sequence
Every connected subset of R is an interval
The Real line R is connected
Every interval is connected
In R, intervals and only intervals are connected.
A subset E of R is connected iff E is an interval
compactness in Real Analysis
Connectedness in Real Analysis
Compactness in topology
Connectedness in topology
compactness
connectedness
theorems of compactness
theorems of connectedness
Heine-Borel theorem
Closed Set | definition | theorems
set is closed iff its complement is open
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

Keep Watching

OMG Maths
Classes by Cheena Banga

Definition of metric Space
Examples of metric space
Open and Closed sets
Topology and convergence
Types of metric spaces
Complete Spaces
Bounded and complete bounded spaces
Compact spaces
Locally compact and proper spaces
connectedness
Separable spaces
Pointed Metric spaces
Types of maps between metric spaces
continuous maps
uniformly continuous maps
Lipschitz-continuous maps and contractions
isometries
Quasi-isometries
notions of metric space equivalence
Topological properties
Distance between points and sets
Hausdorff distance and Gromov metric
Product metric spaces
Continuity of distance
Quotient metric spaces
Generalizations of metric spaces
Metric spaces as enriched categories

Рекомендации по теме

Комментарии

You can download PDF from:
Related Playlist: Limit and Continuity

Please like, Share and Comment.

OMGMaths

Simple and smart explanation mam Thanks for uploading this theorem

praneeth

Wow what a nice explanation!
Thanks for it 😊

shivbirthlia

Nicely explained maam
Thank you so much 🙏

Notfound-ie

Yahi open set k Liye Jo kia hova apny uska link kahn h??

mehwishjabbarjabbar

Mam connected set ka bary ma bi video bana da

devilhed

Mam, I have one doubt.
If a set is closed then the complement is open but If a set is open then the complete of this set is closed whenever set is on bounded. But you have say the complement of open set is closed.but where is boundedness occur??? How the complement of open set is closed??? Plz mam 🙏🏻clear my doubt. Plz plz🙏🏻

s.s

mam bhoot bhoot shukria bhot acha smjhaya i like it and subscribed and completelly watched jakillah

aniqa

Ma'am, is this theorem how you proved for metric space is applicable for two topological space

tapashchowdhury

Thanks very much madam !
huge respect from Islamabad, Pakistan.

muhammadail

Love you mam you are one of the best talented girl

pramodpaswan

f is continuous iff f inverse C is closed set in X for every closed set C in Y | Real Analysis

f is continuous iff f^(-1) (F) is closed in M_1 whenever F is closed in M_2

f is continuous iff f inverse C is closed set in X for every closed set C in Y | Real Analysis

f is continuous iff f(¯A)⊆ ¯(f(A)) for all A ⊆M_1.

f is continuous iff ( f(clA) ⊂ cl f(A) ) - Equivalent definition of continuity in Topology

A function f is continuous iff (x_n )⟶a ⇒ (f(x_n ))⟶f(a).

F is continuous iff inverse image of every open set is open/part 2

A Function from X to Y is Continuous iff for every open set V in Y f–1(V) is open in X

Proof: (f is Continuous) iff ( f-1 int B ⊂ int f-1 B)

6. f is continuous iff f(cl(A)) is subset of cl(f(A)) for every subset of X || Continuity in metric

Continuity of function | Theorem | f is Continous iff f (Ā) is subset closure of f(A) | metric space...

f is continuous iff inverse image of every member of base is open| continous functions | Topology

A Function is Continuous iff The Preimage of a Set in the Codomain is open in the Domain Topology

Theorem|A Function is Continuous iff For Any Subset of Y inverse(intA) is Subset of int[inversef(A)]

Prove that f is continuous iff each of the functions f1,f2,f3...fk is continuous. REAL ANALYSIS

Proof: f(x) = x is Continuous using Epsilon Delta Definition | Real Analysis Exercises

Theorem on continuity of function | Metric Space | Real analysis

Result of Continuous function | L5 | TYBSc Maths | Continuous Functions @ranjankhatu

Sequential Criteria of continuous function | L2 | TYBSc Maths | Continuous Functions @ranjankhatu

Lecture 31 | A map f is continuous iff for any subset A, f(A) is a subset of cl(f(A)) | Topology

Functional Analysis | Linear functional F is Continuous iff kerf is closed | Mrs Cheema

# 8, f is continuous iff inverse image of a closed set is closed in metric space

A function f is continuous on X iff subset A of X, f(A closure) is subset of whole closure of f(A)

A mapping f is continuous iff inverse of f(V) is open in X for every open set V in Y.

A mapping f is continuous iff inverse of f(C) is closed in X for every closet set C in Y.