"A point p is said to be the limit point of a subset A of a topological space X ,if for every open set containing p also contains a point of A other than p" Example. Take X={a,b,c,d,e} and A={a,b,c} topology on X is{phi,X,{a},{c,d},{a,c,d},{b,c,d,e}} Then clearly {e} is a limit point of A, although it does not belong to set A
You are wrong. Limit point of a set A can also belong to A. Let A= {a,b,c}, X={a,b,c,d} T={ {}, X {a},{a,b}, {a,b,c}} Clearly a is a limit point of A, since {{a,b}/{a}}^{a,b,c}=b Which is also belongs to A.
3€x then the open sets containing 3 are (x) only. So ,( ^ means intersection) X-3 ^ A = ({1,2,4,5,6}-3) ^ A = 1,2,4,5,6 ^ 2,3,4 = 2,4 So 3 is a limit point
way of presentation is very good but you have given incorrect definition of limit point and closure you find by you are incorrect as this is equal to X={1,2,3,4,5,6}. First you study the basic clearly and then the upload videos.
limit point set ko belong kar bhi skta hy aor nahi bhi ap ye kah rhy hy limit point woh element nhiho skty jo A ky member hy. That's wrong. limit point may be in set A which is subset of X or not.
Main b ghnty sy khup rha hn sir mistake kr gy Hain Q k closure of Set is a set of intersection of All supersets of A . And JB superset lyty Hain to just X khud hi aata hy
InshaAllah koshish karon ga,,,,,or ap meri topology ka lectures visit karain k shaid ye theorem ho sakta hai k may nay upload kia ho ,,,,,thanks for comment
But ek or doubt hai Jo^pi/2 =1 J ke niche zero hai or ye question real analysis ka hai agr ho sake to please mre assignment ka last date Sunday ko h but abi tk ye nai bna hai
Ap ka method bohat simple and acha ha again jazak Allah
Hafiz Sajid Ishaq
Your starting way of lecture( with the name of Allah) is very very very nice👍.. May Allah Pak give you Success in every fields of life
"A point p is said to be the limit point of a subset A of a topological space X ,if for every open set containing p also contains a point of A other than p"
Example.
Take X={a,b,c,d,e} and A={a,b,c} topology on X is{phi,X,{a},{c,d},{a,c,d},{b,c,d,e}}
Then clearly {e} is a limit point of A, although it does not belong to set A
Best thing is starting with God name and leacture explanation is also very clear and good thanks sir😊
Allah aapko mzeed traqi dy
You are wrong.
Limit point of a set A can also belong to A.
Let A= {a,b,c}, X={a,b,c,d}
T={ {}, X {a},{a,b}, {a,b,c}}
Clearly a is a limit point of A, since {{a,b}/{a}}^{a,b,c}=b
Which is also belongs to A.
sir according to definition es intersection atta ha...
so nice method of teaching..
Thanks
Bhi Ring theroy per bi vedio upload kry thanks.
You are a best teacher. Thank you sir.
Thank you sooo much sir bhutt acha smjhaya 👍🤗
JAI HIND SIR 🇮🇳 Good explains
3€x then the open sets containing 3 are (x) only.
So ,( ^ means intersection)
X-3 ^ A = ({1,2,4,5,6}-3) ^ A = 1,2,4,5,6 ^ 2,3,4 = 2,4
So 3 is a limit point
Sir 6 is also the limit point of A
Asslamoalaikum sir ap knsi book sy topology k lecture dy rhy hain
Sir is trah to sbi points jo set a ma ha in k ilawa limit point hon gay
Expalanation is so nice sir i understand it
Jazak Allah sir so much
Best solution.....keep it up !
Good
Thanks
Sir aap Kisi college main perha rehy
Sir compactness and connectedness pr bi Ak lecture day dayn
Thank u your method is too good.
Aqsa Maqsood .... Thanks
Ustaad can you present it in English? If yes plz do so. Thanks
Sir plz adherent point ki video b upload krdo with eg.
way of presentation is very good but you have given incorrect definition of limit point and closure you find by you are incorrect as this is equal to X={1,2,3,4,5,6}. First you study the basic clearly and then the upload videos.
Ohh thats why I always got confused whenever I study limit points bec I watched this nd got concept of limit pts from this😢
Sir maazrt k sath Answer X aata hy
Q k Closure of Set is the intersection of all supersets of A
According to defination
Correct me if im wrong
Thank you sir
Thanks. But definition b dia krn
limit point set ko belong kar bhi skta hy aor nahi bhi ap ye kah rhy hy limit point woh element nhiho skty jo A ky member hy.
That's wrong.
limit point may be in set A which is subset of X or not.
Agree
Agree
Agreeeee...
Bhut Shandar
Thank you! Sir
السلام عليكم
أتمنى انك تشرحها باللغة العربية
وشكرا
thank u so much sir
sir it's very clear thank you😊
You are giving a wrong definition of limit point
where i m wrong in this presentation and described what is the correct definition of limit point....
Here 6 is also a limit point
good
Thank u soo much sir
Jazakal Allah
sir you are giving wrong defination.
closure set is the intersection of all the closed supersets of A.
don't understand
Sir X contain the point x
Ap k es lecture n pechly sary concept he wrong kr diya
Thank you sir..
sir please more class lecture
Iss k answer x e atta hn sir app ny wrong kia hn
Main b ghnty sy khup rha hn sir mistake kr gy Hain
Q k closure of Set is a set of intersection of All supersets of A . And JB superset lyty Hain to just X khud hi aata hy
Chatur Ramalingam Lite (2.0)
NC ,I understand
:)
Fazoool pechly concept bhi khrab kr dia
In any topological space, prove that A' = A ᴗ D (A) any one please solve this
InshaAllah koshish karon ga,,,,,or ap meri topology ka lectures visit karain k shaid ye theorem ho sakta hai k may nay upload kia ho ,,,,,thanks for comment
Ha mil gya thank you
But ek or doubt hai
Jo^pi/2 =1
J ke niche zero hai or ye question real analysis ka hai agr ho sake to please mre assignment ka last date Sunday ko h but abi tk ye nai bna hai
J kia hai ,,,,,,, ye even number hai ya odd number hai,,,,,,,,,please ap ye bta dain k J ki jaga kon sa number hai
Sir 3 is also a limit point