Question

Does the intersection of two dense, open sets have the Baire property?

score 92 · Answer 1 · 2026-03-25 20:10:58

92

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Does the intersection of two dense, open sets have the Baire property?

Published on 25 Mar 2026 - 20:10

score 1.9k · Answer 2 · 2026-04-02 02:08:08

1.9k

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Every inner product space is a metric space.

Published on 02 Apr 2026 - 2:08

score 71 · Answer 3 · 2026-03-28 23:16:37

71

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Is there a name for the function $D(x,y) = \sum\limits_{i = 1}^n (x_i - y_i)$, where $x$ and $y$ are vectors in $\mathbb{R}^n$?

Published on 28 Mar 2026 - 23:16

score 30 · Answer 4 · 2026-03-26 22:55:37

30

Views

Prove that $f \in R(F_s)$ on the interval $[a, b]$ and that $\int f dF_s = f(s)$

Published on 26 Mar 2026 - 22:55

score 56 · Answer 5 · 2026-03-26 09:38:06

56

Views

When does it make sense to find a point between two points?

Published on 26 Mar 2026 - 9:38

score 101 · Answer 6 · 2018-12-07 00:59:37

101

Views

Find a metric $d$ on $\mathbb{N}$

Published on 07 Dec 2018 - 0:59

score 308 · Answer 7 · 2026-03-25 21:01:33

308

Views

Proving that the non-negative real line is complete

Published on 25 Mar 2026 - 21:01

score 438 · Answer 8 · 2026-03-25 23:56:33

438

Views

How to find a completion for a metric space (For instance, support compact continuous real functions)

Published on 25 Mar 2026 - 23:56

score 28 · Answer 9 · 2018-12-07 15:29:20

28

Views

Open and closed subgroups of continous functions with max metric

Published on 07 Dec 2018 - 15:29

score 75 · Answer 10 · 2018-12-07 17:26:40

75

Views

In usual Euclidean metric on $\mathbb{R}^n$. Which of the following metric spaces X is complete

Published on 07 Dec 2018 - 17:26

score 86 · Answer 11 · 2026-03-29 11:50:09

86

Views

Is it possible to represent an open and connected set in $(\mathbb{R}^n,||\cdot||)$ as the finite union of convex sets?

Published on 29 Mar 2026 - 11:50

score 113 · Answer 12 · 2018-12-08 00:48:09

113

Views

If $int\overline{X} = int\overline{Y} = \emptyset$ then $int(\overline{X\cup Y}) = \emptyset$.

Published on 08 Dec 2018 - 0:48

score 2k · Answer 13 · 2018-12-08 13:32:58

2k

Views

Is it true that every totally bounded set in a metric space is compact?

Published on 08 Dec 2018 - 13:32

score 186 · Answer 14 · 2026-03-25 12:20:54

186

Views

Countable open cover up to a null set

Published on 25 Mar 2026 - 12:20

score 694 · Answer 15 · 2018-12-09 19:26:30

694

Views

What are some advanced books on metric space?

Published on 09 Dec 2018 - 19:26

List Question

Does the intersection of two dense, open sets have the Baire property?

Every inner product space is a metric space.

Is there a name for the function $D(x,y) = \sum\limits_{i = 1}^n (x_i - y_i)$, where $x$ and $y$ are vectors in $\mathbb{R}^n$?

Prove that $f \in R(F_s)$ on the interval $[a, b]$ and that $\int f dF_s = f(s)$

When does it make sense to find a point between two points?

Find a metric $d$ on $\mathbb{N}$

Proving that the non-negative real line is complete

How to find a completion for a metric space (For instance, support compact continuous real functions)

Open and closed subgroups of continous functions with max metric

In usual Euclidean metric on $\mathbb{R}^n$. Which of the following metric spaces X is complete

Is it possible to represent an open and connected set in $(\mathbb{R}^n,||\cdot||)$ as the finite union of convex sets?

If $int\overline{X} = int\overline{Y} = \emptyset$ then $int(\overline{X\cup Y}) = \emptyset$.

Is it true that every totally bounded set in a metric space is compact?

Countable open cover up to a null set

What are some advanced books on metric space?

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