Question

Show the set $\{x \in M: f(x)<g(x)\}$ is an open set in metric space when $f,g$ are continuous

score 1.3k · Answer 1 · 2026-04-12 22:58:31

1.3k

Views

Show the set $\{x \in M: f(x)<g(x)\}$ is an open set in metric space when $f,g$ are continuous

Published on 12 Apr 2026 - 22:58

score 70 · Answer 2 · 2026-04-14 20:25:12

70

Views

Prove that $ρ$ induces a continuous function from $S^n → O(n+1)$ and therefore from $\Bbb RP^n → O(n+1)$

Published on 14 Apr 2026 - 20:25

score 29 · Answer 3 · 2026-04-12 12:43:18

29

Views

Reference about torus

Published on 12 Apr 2026 - 12:43

score 925 · Answer 4 · 2026-04-17 03:41:15

925

Views

Proof that the boundary of the square is not an embedded submanifold

Published on 17 Apr 2026 - 3:41

score 238 · Answer 5 · 2026-04-17 14:23:30

238

Views

Bourbaki's Mittag-Leffler theorem

Published on 17 Apr 2026 - 14:23

score 81 · Answer 6 · 2026-04-14 05:29:40

81

Views

Can one state and prove that Euclidean space has genus $0$ in Hilbert's geometry?

Published on 14 Apr 2026 - 5:29

score 179 · Answer 7 · 2026-04-16 06:54:49

179

Views

$A + B = \{\,x + y \mid x ∈ A,\, y ∈ B\,\}$ is closed in $ [0,\infty)$ for any closed $A, B \subseteq [0,∞)$

Published on 16 Apr 2026 - 6:54

score 1.5k · Answer 8 · 2026-04-13 07:59:06

1.5k

Views

The relationship between the differential and the directional derivative of a function

Published on 13 Apr 2026 - 7:59

score 73 · Answer 9 · 2026-04-10 16:18:15

73

Views

Existence of unique measure

Published on 10 Apr 2026 - 16:18

score 227 · Answer 10 · 2026-04-09 14:15:13

227

Views

Continuous function on Hausdorff space

Published on 09 Apr 2026 - 14:15

score 46 · Answer 11 · 2026-03-25 06:24:31

46

Views

Separable $\Rightarrow$ Lindelöf for metric spaces without using second-countability

Published on 25 Mar 2026 - 6:24

score 279 · Answer 12 · 2026-04-15 03:41:16

279

Views

Does there exist a continuous path between two sets of oriented basis for a vector space out of a collection of subspaces?

Published on 15 Apr 2026 - 3:41

score 118 · Answer 13 · 2026-04-17 07:09:59

118

Views

When can an open set be written as a finite number of disjoint open intervals?

Published on 17 Apr 2026 - 7:09

score 63 · Answer 14 · 2026-04-15 08:47:09

63

Views

Group Actions on $\Bbb R^n$

Published on 15 Apr 2026 - 8:47

score 98 · Answer 15 · 2026-04-21 15:24:34

98

Views

Show the hypercube $[a,b]^n$ is closed

Published on 21 Apr 2026 - 15:24

List Question

Show the set $\{x \in M: f(x)<g(x)\}$ is an open set in metric space when $f,g$ are continuous

Prove that $ρ$ induces a continuous function from $S^n → O(n+1)$ and therefore from $\Bbb RP^n → O(n+1)$

Reference about torus

Proof that the boundary of the square is not an embedded submanifold

Bourbaki's Mittag-Leffler theorem

Can one state and prove that Euclidean space has genus $0$ in Hilbert's geometry?

$A + B = \{\,x + y \mid x ∈ A,\, y ∈ B\,\}$ is closed in $ [0,\infty)$ for any closed $A, B \subseteq [0,∞)$

The relationship between the differential and the directional derivative of a function

Existence of unique measure

Continuous function on Hausdorff space

Separable $\Rightarrow$ Lindelöf for metric spaces without using second-countability

Does there exist a continuous path between two sets of oriented basis for a vector space out of a collection of subspaces?

When can an open set be written as a finite number of disjoint open intervals?

Group Actions on $\Bbb R^n$

Show the hypercube $[a,b]^n$ is closed

Trending Questions

Popular # Hahtags

Popular Questions