Theorem of connectedness | Connectedness | Real analysis | Metric space | topology | Compactness

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
Theorem | Compactness | Connectedness | Compact set | Connected sets | Real Analysis | Metric Space | Topology | connectedness in Real Analysis | Point set topology | math tutorials | Classes By Cheena Banga.
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Other topics covered in playlist:
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
Math Tutorials
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
Compactness in Real analysis
compactness in metric space
compactness in topology
compactness and connectedness in real analysis
compactness and connectedness
compactness in topological space
Connectedness in Real analysis
connectedness in metric space
connectedness in topology
connectedness in topological space
Theorems on connectedness
theorems on compactness
Theorems of connectedness
theorems of compactness

[@infinityskylines6548]

This theorem is explained very well... Thank you ✨

[@OMGMaths]

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[@Sangul2829]

Wow, first time I understand topology, thanks alot ma'am for such wise explanation.

[@OMGMaths]

My pleasure 😊

[@OMGMaths]

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[@chandrmohankushwaha5156]

Wow what a explain

[@OMGMaths]

Thank You 😊 subscribe and press 🔔 for updates.

[@mansi4122]

Nice thankyou mam❤❤

[@OMGMaths]

thank you please keep watching and sharing..

[@user-pd4fd5hh2c]

Thankew mam❤

[@OMGMaths]

Most Welcome 😊 If you're finding my math lessons helpful and engaging, I kindly request you to share them with your fellow students, classmates, and anyone who could benefit from a little mathematical magic. Together, let's make learning math a fun and exciting journey!

[@uditnarayan1360]

Excellent explanation. I am a MS scholar in the CSE deapartment of IITM but I have to take real analysis course from mathematics department as it was required for my research. Trust me, the proff was not able to explain it this clearly 😅. Thanks a lot.

[@haritakashyap387]

Awesome ma'am.

[@pushkarkumar3089]

So easily proved!!!! Many~many thanks!!!!

[@OMGMaths]

Thank you 🙏 Keep Watching … Please Share with Others…

[@pushkarkumar3089]

@@OMGMaths 👍

[@naziyanavas1780]

Thank you for explaining this theorem very well.

[@OMGMaths]

Glad it was helpful! Please write your valuable reviews at g.page/r/CRP90Pt3uFhFEAg/review

[@yatharthagoldi88]

Thank you mam it helped me alot😇

[@mudassargondal1904]

Very good explanation

[@BeTheSiriusStar]

Thank you mam 🙏🙏🙏

[@OMGMaths]

Most welcome 😊

[@tarikhasan374]

Thanks a lot Mam.

[@OMGMaths]

Most welcome 😊 If you're finding my math lessons helpful and engaging, I kindly request you to share them with your fellow students, classmates, and anyone who could benefit from the content.

[@akashprusty4352]

Nicely explained

[@OMGMaths]

Thank You 😊 Your appreciation means a lot lot for me….Please write your valuable reviews at g.page/r/CRP90Pt3uFhFEAg/review Like ,share and Subscribe.

[@Rashi_sharma0001]

Thank u so much 🙂

[@chandarani710]

Mam 1st theorem ma ap ny strt clouser of A intersection B lia lkin property ap NY A intersection B dono clouser wlly liye Ksy ma'am

[@abhaygupta4461]

Thanks mam

[@chandarani710]

Mam Algebra ppr k theorem krwa dyn

[@dipsaha6178]

"X is a connected matric space suppose X has atleast two points then X is uncountable" Mam iska proof kayse kare?

[@keshavlalit1555]

Mam agar d A closure ki boundary. Per hota toh d belong kr jaata B me or A me belong nhi karta ,kya ye possible nhi h

[@nishajoshi2280]

Thank you maam

[@OMGMaths]

Welcome 😊 "subscribe" and press bell for updates. you can also find more video on "compactness and connectedness" on kzbin.info/aero/PLYisSyPLgRv56AS8iI91P3CIlhrzpKSJO

[@madan8882]

Thanks

[@bishalsaha3688]

Dense set koriye

[@bishalsaha3688]

Separable space koraiye mamm

[@jagdishexcellentgadhvijayg2458]

Separated sets are always disjoint

[@OMGMaths]

kzbin.info/www/bejne/Z6HIk6Bta6l6Ztk separated sets are disjoint.(video link)

[@ShamimKhadiagala]

You people we want to understand but your language.....😮

[@bhaisashravani]

Thank you mam ❤