Sir... Base or subbase me phi hona chahiye . Isse pehle wale video me maeine comment kia tha. Ki phi (open set )bhi kisi element ka union hona chahiye jo ki base me ho . phir phi sub base me bhi hona chahiye kyuki (((( phi or subbase ke kisi bhi element ka intersection phi hoga.)))). Or yeh base me hoga. In sort sir ,mere hissab se phi alag se base or subbase me hona chahiye. 🙂
(X,T) discrete topology T1={{a,b}, (b,c),(c,a) } is not base for T ,but is it subbase sir True or false sir Means if any subset of T is not base but may be it subbase
Sir in the last example, if I donot take all the unions of sets in T1 but take only a few of them so that they form a topology, then also can we say that T1 is a base for it? For example if I take T={phi, X, {b}, {d}, {b,d}}, then T is a topology on X and each of the elements of T is a union of elements of T1. Am I correct?
Sir, I have a question that a sub-base can have phi?....I think no.... Because sir, intersection with phi is always makes phi, then sub-base can never make a base, I.e. that is not a sub-base which can't make a base..... Am I right sir?
Sir Maja aa gya sare concepts samajh aane lage
Sir Aapke prayas se hum BHI bahut Kuch Sikh Gaye 🙏🙏🙏🙏🙏🙏🙏🙏
Sir... Base or subbase me phi hona chahiye . Isse pehle wale video me maeine comment kia tha.
Ki phi (open set )bhi kisi element ka union hona chahiye jo ki base me ho .
phir phi sub base me bhi hona chahiye kyuki (((( phi or subbase ke kisi bhi element ka intersection phi hoga.)))).
Or yeh base me hoga.
In sort sir ,mere hissab se phi alag se base or subbase me hona chahiye.
🙂
Allah ap ko Happy and healthy rakhy sir g
Thank you so much sir.🙏🏻
Thanku sir.. Onek upokrito holam
Thank you
👏👏🎉
Same elements ka same elements se intersection le skte hai ky
सर आपने बहुत ही अच्छा बताया मुझे तुझे समझ में नहीं आ रहा था यहां तक की मेरे बुक में से गलत लिखा था HK पाठक की किताब मे।
Super explanation sirji 👌👌👌👌
Thank you
Nice explain sir 🙏🙏
Very nice class sir
(X,T) discrete topology
T1={{a,b}, (b,c),(c,a) } is not base for T ,but is it subbase sir
True or false sir
Means if any subset of T is not base but may be it subbase
Fantastic explanation as always
Thank you
Sir please SUBBASE ka ek aur example bta dijiye jisme poora X include na ho 🥺🙏
Sir please 🙏
For example Sir X={a,b,c,d} and T={phi,{a},{a,c},{a,d},{a,c,d},X} and T1= {{a,d},{a,c}} is a sub base for T ?
Ok ok definitely
!! EXCELLENT 👌👍👍. what is the difference between usual topology and base of usual topology
Please go ahead u will get answer of every question
Thanks sir for the nice explanation
Welcome
Good explanation sir
Sir Alexander sub base theorem explain
Very nice teaching thanku
Welcome
❤
Superb thnku sir
Welcome
Thank you sir
Please sir connectedness ki videos send karyee
Yes very soon please wait thank you
Sir in the last example, if I donot take all the unions of sets in T1 but take only a few of them so that they form a topology, then also can we say that T1 is a base for it?
For example if I take
T={phi, X, {b}, {d}, {b,d}}, then T is a topology on X and each of the elements of T is a union of elements of T1. Am I correct?
I will reply when I am free
@@HDMATHEMATICSBYHDSIR Ok sir.
Nice sir ji
Thank you
Verify that 𝑆 = {(𝑎, ∞) | 𝑎 ∈ 𝑅} ∪ {(−∞, 𝑎) | 𝑎 ∈ 𝑅} is a subbasis for the standard topology on R. Sir ya theorem plzz kar da
Sir Jo subbase Se basis form hoga wo unique hoga ya Nahi?
Yes unique
Thank u
Sir, I have a question that a sub-base can have phi?....I think no.... Because sir, intersection with phi is always makes phi, then sub-base can never make a base, I.e. that is not a sub-base which can't make a base..... Am I right sir?
No Rajat , actually u seeing intersection with only phi but intersection with other elements gives some element not phi .
No , as we consider every sub base of T is also contains base for T
Sometimes Both are equal
Thank you for ji
Brilliant
Thank you
Sir, it's my humble request to sort all videos on topology in one playlist and name that by Topology. And for other videos follow the same trend
@@exploreyourself6002 ok it is already in a playlist please go to playlist u will get many topics
Thank you
Prove that space is 2nd countable iff it has a countable subbase
Ok please wait
@@HDMATHEMATICSBYHDSIR ok sir