jpv

Hyderabad, India

Jul
17
awarded Inquisitive
Jul
17
comment Basic Question about notation in the space of continuous functions
In the second edition of the book, it seems the functions are assumed to be bounded, as user161825 pointed out.
Jul
16
comment Ascoli-Arzela Theorem
Thanks for the comment.
Jul
16
asked Ascoli-Arzela Theorem
Jul
12
comment Cartesian product of compact sets is compact
In the general case, this is known as Tychonoff's Theorem.
Jul
11
awarded Yearling
Jul
11
awarded Yearling
Jul
8
accepted Basic Question about notation in the space of continuous functions
Jul
8
comment Basic Question about notation in the space of continuous functions
Thanks for the answer and the suggestion. I could not find any book by Brezis and Evans, could you give the title of the book. Thanks.
Jul
6
asked Basic Question about notation in the space of continuous functions
Jul
2
awarded Curious
Jul
1
comment Partition of Unity
Thanks for the answer.
Jul
1
accepted Partition of Unity
Jun
29
asked Partition of Unity
Jun
29
accepted Measure on Locally Compact, Separable metric space
Jun
29
comment Measure on Locally Compact, Separable metric space
I found the way: A separable metric space is Lindelof. Now, $X$ can be covered by a union of balls centered at every point of $X$. These balls are taken from the local compactness of $X$. This way, we get a countable cover of $X$ by the balls and hence by the compact sets.
Jun
26
comment Measure on Locally Compact, Separable metric space
Tom: I was unable to find a proof of this. Could you provide a reference?
Jun
25
comment Measure on Locally Compact, Separable metric space
Tom: Thanks for the edit. I think this proves. I hope I will be able to get a proof of this somewhere.
Jun
25
comment Measure on Locally Compact, Separable metric space
Tom: In this case, I am not sure how to show that $X=\cup_{i=1}^\infty U_i$.
Jun
25
asked Measure on Locally Compact, Separable metric space
1 2 3 4 5