Question

Prove that the topology of R^2 is the same as the topology of the the cartesian product RxR

score 1.2k · Answer 1 · 2018-01-18 21:12:52

1.2k

Views

Prove that the topology of R^2 is the same as the topology of the the cartesian product RxR

Published on 18 Jan 2018 - 21:12

score 55 · Answer 2 · 2018-01-18 22:30:16

55

Views

How to show that arc on $S^{1}$ specified by continuous range of angles $[0,\pi)$ is not open or closed set

Published on 18 Jan 2018 - 22:30

score 163 · Answer 3 · 2026-03-22 14:17:23

163

Views

Sequence in $B[0,1]\subset L^2[0,1]$ which has no convergent subseqence.

Published on 22 Mar 2026 - 14:17

score 94 · Answer 4 · 2026-03-16 22:09:05

94

Views

Is the following metric?

Published on 16 Mar 2026 - 22:09

score 104 · Answer 5 · 2026-03-20 05:01:26

104

Views

What is the set $\{M \subset \mathbb{R}^n| M^{af} \subsetneq M^f\}$?

Published on 20 Mar 2026 - 5:01

score 54 · Answer 6 · 2018-01-19 07:29:51

54

Views

The "topological structure" of the tuples of images and preimages of a function

Published on 19 Jan 2018 - 7:29

score 39 · Answer 7 · 2018-01-19 07:56:09

$ \tau _{f} = \lbrace A \subset Y: f^{-1}(A) \in \tau \rbrace $. Show that $ A $ is open in $ Y $ if and only if $ f^{-1}(A) $ is open in $ X $ .

score 1.1k · Answer 8 · 2026-03-25 20:59:53

1.1k

Views

Separability of Hilbert/vector space and its countable basis

Published on 25 Mar 2026 - 20:59

score 928 · Answer 9 · 2026-03-24 07:58:57

928

Views

Why are functions of compact support so important?

Published on 24 Mar 2026 - 7:58

score 135 · Answer 10 · 2026-03-22 06:47:03

135

Views

Are there analogues to orthogonal transformations in non-orientable surfaces?

Published on 22 Mar 2026 - 6:47

score 623 · Answer 11 · 2018-01-19 21:07:46

623

Views

Special triangulations for the torus, Klein bottle and real projective plane

Published on 19 Jan 2018 - 21:07

score 1.2k · Answer 12 · 2026-03-17 07:23:56

1.2k

Views

Is Hilbert space a Normed Space or a Inner Product Space? Or it have to be both at the same time?

Published on 17 Mar 2026 - 7:23

score 41 · Answer 13 · 2026-03-20 03:02:21

41

Views

Proof of lemma 1 on "some questions in the theory of bicompactifications" by E. Sklyarenko

Published on 20 Mar 2026 - 3:02

score 238 · Answer 14 · 2026-03-26 15:17:14

238

Views

False proof that $\operatorname{Spec}(\prod_{i=1}^\infty \mathbb F_2)$ is discrete

Published on 26 Mar 2026 - 15:17

score 56 · Answer 15 · 2026-03-25 06:01:55

56

Views

$L^2_{\mathbb{R}}(M)$ is closed in $L^2_{\mathbb{C}}(M)$

Published on 25 Mar 2026 - 6:01

List Question

Prove that the topology of R^2 is the same as the topology of the the cartesian product RxR

How to show that arc on $S^{1}$ specified by continuous range of angles $[0,\pi)$ is not open or closed set

Sequence in $B[0,1]\subset L^2[0,1]$ which has no convergent subseqence.

Is the following metric?

What is the set $\{M \subset \mathbb{R}^n| M^{af} \subsetneq M^f\}$?

The "topological structure" of the tuples of images and preimages of a function

$ \tau _{f} = \lbrace A \subset Y: f^{-1}(A) \in \tau \rbrace $. Show that $ A $ is open in $ Y $ if and only if $ f^{-1}(A) $ is open in $ X $ .

Separability of Hilbert/vector space and its countable basis

Why are functions of compact support so important?

Are there analogues to orthogonal transformations in non-orientable surfaces?

Special triangulations for the torus, Klein bottle and real projective plane

Is Hilbert space a Normed Space or a Inner Product Space? Or it have to be both at the same time?

Proof of lemma 1 on "some questions in the theory of bicompactifications" by E. Sklyarenko

False proof that $\operatorname{Spec}(\prod_{i=1}^\infty \mathbb F_2)$ is discrete

$L^2_{\mathbb{R}}(M)$ is closed in $L^2_{\mathbb{C}}(M)$

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