Saaqib Mahmood's user avatar
Saaqib Mahmood's user avatar
Saaqib Mahmood's user avatar
Saaqib Mahmood
  • Member for 11 years, 1 month
  • Last seen this week
  • Abbottabad, Pakistan
33 votes
2 answers
15k views

How to prove that if a normed space has Schauder basis, then it is separable? What about the converse?

32 votes
2 answers
17k views

How to prove the continuity of the metric function?

24 votes
0 answers
2k views

Theorem 6.17 in Baby Rudin, 3rd ed: $\int_a^b f \,d\alpha = \int_a^b f(x) \alpha^\prime(x) \,dx$

19 votes
1 answer
8k views

Is $\mathbb{R}^\omega$ in the uniform topology connected?

18 votes
1 answer
12k views

About Banach Spaces And Absolute Convergence Of Series

18 votes
3 answers
2k views

Theorem 3.54 (about certain rearrangements of a conditionally convergent series) in Baby Rudin: A couple of questions about the proof

17 votes
5 answers
3k views

Prob. 6 (d), Chap. 1, in Baby Rudin, 3rd ed: How to complete this proof?

17 votes
4 answers
2k views

Prob. 17, Chap. 2, in Baby Rudin: The set of all numbers in $[0,1]$ with only $4$ and $7$ as decimal digits is countable, dense, compact, perfect?

15 votes
6 answers
24k views

Which Mathematical Analysis I Book or Textbook Is The Best?

15 votes
3 answers
20k views

How is every subset of the set of reals with the finite complement topology compact?

14 votes
5 answers
17k views

Can an integer of the form $4n+3$ written as a sum of two squares?

14 votes
1 answer
3k views

Prob. 5, Sec. 20, in Munkres' TOPOLOGY, 2nd ed: What is the closure of $\mathbb{R}^\infty$ in $\mathbb{R}^\omega$ in the uniform topology?

14 votes
1 answer
2k views

Prob. 5, Sec. 27 in Munkres' TOPOLOGY, 2nd ed: Every compact Hausdorff space is a Baire space

14 votes
0 answers
1k views

Theorem 6.12 (a) in Baby Rudin: $\int_a^b \left( f_1 + f_2 \right) d \alpha=\int_a^b f_1 d \alpha + \int_a^b f_2 d \alpha$

13 votes
1 answer
417 views

Prob. 2(b), Sec. 25, in Munkres' TOPOLOGY, 2nd ed: The iff-condition for two points to be in the same component of $\mathbb{R}^\omega$

12 votes
1 answer
1k views

Theorem 6.16 in Baby Rudin: $\int_a^b f d \alpha = \sum_{n=1}^\infty c_n f\left(s_n\right)$

12 votes
0 answers
1k views

Prob. 1, Sec. 27, in Munkres' TOPOLOGY, 2nd ed: How to show that the compactness of every closed interval implies the least upper bound property?

12 votes
7 answers
5k views

Which book to use in conjunction with Munkres' TOPOLOGY, 2nd edition?

12 votes
2 answers
4k views

How is the metric topology the coarsest to make the metric function continuous?

12 votes
1 answer
2k views

How are these definitions of the limit superior and limit inferior equivalent?

11 votes
1 answer
4k views

Is the space $B([a,b])$ separable?

11 votes
4 answers
5k views

How to prove this result involving the quotient maps and connectedness?

11 votes
3 answers
3k views

Theorem 6.10 in Baby Rudin: If $f$ is bounded on $[a, b]$ with only finitely many points of discontinuity at which $\alpha$ is continuous, then

11 votes
1 answer
3k views

Prob. 23, Chap. 4, in Baby Rudin: Every convex function is continuous and every increasing convex function of a convex function is convex

10 votes
2 answers
1k views

Examples 3.35 (a) and (b) in Baby Rudin: Limit Superior and limit inferior of a couple of sequences

10 votes
3 answers
954 views

Prob. 8, Sec. 3.5 in Erwin Kreyszig's Introductory Functoinal Anlaysis With Applications

10 votes
3 answers
2k views

Can a non-zero vector have zero image under every linear functional?

10 votes
2 answers
490 views

Can we conclude that this group is cyclic? [duplicate]

10 votes
3 answers
6k views

How to decide about the convergence of $\sum(n\log n\log\log n)^{-1}$?

10 votes
0 answers
2k views

Prob. 10, Sec. 3.2, in Erwin Kreyszig's "Introductory functional analysis with applications"

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