Question

Why are uniform spaces defined the way they are? What is uniformity saying intuitively?

score 237 · Answer 1 · 2021-09-10 18:27:48

237

Views

Why are uniform spaces defined the way they are? What is uniformity saying intuitively?

Published on 10 Sep 2021 - 18:27

score 44 · Answer 2 · 2021-10-02 19:54:33

44

Views

How to prove in metric space that classical definition of the Cauchy sequence coincides with the entourage definition of the Cauchy sequence?

Published on 02 Oct 2021 - 19:54

score 50 · Answer 3 · 2026-02-23 06:24:23

50

Views

Where can I find more insight about spaces of subsets of a base space?

Published on 23 Feb 2026 - 6:24

score 99 · Answer 4 · 2021-11-28 18:38:29

How to prove that there is an entourage $V$ such that $V(B) \cap A = \emptyset$ in a uniform space when A is compact and B is closed?

score 63 · Answer 5 · 2021-12-07 10:27:21

63

Views

Necessary and suficient condition for a uniform space to be complete

Published on 07 Dec 2021 - 10:27

score 249 · Answer 6 · 2022-01-04 19:45:12

249

Views

Intuition for a uniform space?

Published on 04 Jan 2022 - 19:45

score 73 · Answer 7 · 2022-01-05 19:19:05

73

Views

Neighborhood base generated by uniformity

Published on 05 Jan 2022 - 19:19

score 13 · Answer 8 · 2022-01-10 22:08:13

13

Views

Proximity to an arbitrary family and compact space

Published on 10 Jan 2022 - 22:08

score 85 · Answer 9 · 2022-01-17 16:21:39

85

Views

What are uniform spaces actually useful for?

Published on 17 Jan 2022 - 16:21

score 118 · Answer 10 · 2022-01-23 17:05:16

118

Views

Quibble with proofs of the compact-open topology being equivalent to the uniform convergence topology: what happens if $f(x)$ is an isolated point?

Published on 23 Jan 2022 - 17:05

score 29 · Answer 11 · 2022-01-25 18:28:55

29

Views

Entourage asymmetry and Cauchy nets: $x_a$ is $V$-close to $x_b$ does not imply $x_b$ is $V$-close to $x_a$

Published on 25 Jan 2022 - 18:28

score 37 · Answer 12 · 2022-02-17 15:23:52

37

Views

Certain properties of uniform structure

Published on 17 Feb 2022 - 15:23

score 31 · Answer 13 · 2022-03-01 10:41:12

31

Views

Contraction principle type theorems for uniform spaces

Published on 01 Mar 2022 - 10:41

score 115 · Answer 14 · 2022-04-18 07:35:18

115

Views

Does every net has a convergent subnet in a compact uniform space?

Published on 18 Apr 2022 - 7:35

score 128 · Answer 15 · 2023-01-25 22:44:08

128

Views

Is a filter generated by a Dedekind cut a minimal Cauchy filter and vice versa?

Published on 25 Jan 2023 - 22:44

List Question

Why are uniform spaces defined the way they are? What is uniformity saying intuitively?

How to prove in metric space that classical definition of the Cauchy sequence coincides with the entourage definition of the Cauchy sequence?

Where can I find more insight about spaces of subsets of a base space?

How to prove that there is an entourage $V$ such that $V(B) \cap A = \emptyset$ in a uniform space when A is compact and B is closed?

Necessary and suficient condition for a uniform space to be complete

Intuition for a uniform space?

Neighborhood base generated by uniformity

Proximity to an arbitrary family and compact space

What are uniform spaces actually useful for?

Quibble with proofs of the compact-open topology being equivalent to the uniform convergence topology: what happens if $f(x)$ is an isolated point?

Entourage asymmetry and Cauchy nets: $x_a$ is $V$-close to $x_b$ does not imply $x_b$ is $V$-close to $x_a$

Certain properties of uniform structure

Contraction principle type theorems for uniform spaces

Does every net has a convergent subnet in a compact uniform space?

Is a filter generated by a Dedekind cut a minimal Cauchy filter and vice versa?

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