Metric Spaces | Lecture 49 | If Complement of any set is Open then it contains all its limit Points

[@menereokon1254]

Thank you very much. The diagram was really helpful.

[@venum1773]

sir, if X-F is open, then we can say F is closed and all the points in a closed set contain their own limit points, i.e, closed set F=F'. Can we use that property to make this short?

[@ranjankhatu]

@@venum1773 sure. But to get marks in exam, students should write answer with proper length. In topology, there are multiple ways to prove any result.

[@venum1773]

@@ranjankhatu thanks sir, really appreciate your videos, arguably the best series on Metric spaces on UA-cam.

[@educationfreely6122]

👍👍👍👍 next level explanation

[@ranjankhatu]

Thank you

[@yashghuge8760]

if x is limit point of F then it is automatically belongs to F then why we take x not belongs to F

[@ranjankhatu]

If x is limit point of F then it need not in F. But here we have to prove it. We start the proof here by considering exactly opposite statement. Therefore we started the proof by considering x does not belong to F