Question

$U$ be the set of all $2×2$ matrices with real entries such that all their eigenvalues belong to $C - R $, and $X = M_2(R)$. Is $U$ open?

score 724 · Answer 1 · 2026-04-15 20:24:52

724

Views

$U$ be the set of all $2×2$ matrices with real entries such that all their eigenvalues belong to $C - R $, and $X = M_2(R)$. Is $U$ open?

Published on 15 Apr 2026 - 20:24

score 366 · Answer 2 · 2026-04-13 22:00:06

366

Views

Metrisability is hereditary property

Published on 13 Apr 2026 - 22:00

score 136 · Answer 3 · 2026-05-11 02:19:43

136

Views

Defining the $p$-adic metric on $\mathbb{Z}$

Published on 11 May 2026 - 2:19

score 179 · Answer 4 · 2026-05-10 20:00:30

179

Views

Continuous function from metric space to R

Published on 10 May 2026 - 20:00

score 139 · Answer 5 · 2026-05-10 16:02:21

139

Views

Prove that a length-minimizing path in a metric space is injective

Published on 10 May 2026 - 16:02

score 586 · Answer 6 · 2026-04-13 04:21:54

586

Views

Closed ball is a closed set

Published on 13 Apr 2026 - 4:21

score 35 · Answer 7 · 2026-05-11 09:15:12

35

Views

Let $p$ be a point in $X$ at which $f(p) \gt 0$ Show there is some positive number $r$ such that $f(q) \gt 0$ for all q in $B_r(p)$

Published on 11 May 2026 - 9:15

score 1k · Answer 8 · 2026-05-10 19:16:41

1k

Views

Lipschitz functions form a Banach space, and Analyzing its Dual

Published on 10 May 2026 - 19:16

score 76 · Answer 9 · 2026-04-12 08:35:28

76

Views

About completing metric spaces

Published on 12 Apr 2026 - 8:35

score 61 · Answer 10 · 2026-05-10 14:30:27

61

Views

Rank Preserving Maps between Metric Spaces

Published on 10 May 2026 - 14:30

score 40 · Answer 11 · 2026-04-10 10:54:38

40

Views

A compact subset question

Published on 10 Apr 2026 - 10:54

score 50 · Answer 12 · 2026-05-11 05:44:57

50

Views

Consider $B\subset\Re^{n}$ a ball (open or closed). Show that for all $x\in B$, the set $B-\{x\}$ is connected.

Published on 11 May 2026 - 5:44

score 178 · Answer 13 · 2026-04-16 10:53:19

178

Views

To show a metric space is complete

Published on 16 Apr 2026 - 10:53

score 99 · Answer 14 · 2026-04-16 18:03:31

99

Views

Metric Topology: Collection of $B_d(x,\epsilon)$?

Published on 16 Apr 2026 - 18:03

score 185 · Answer 15 · 2026-04-09 04:00:14

185

Views

Diameter closure set

Published on 09 Apr 2026 - 4:00

List Question

$U$ be the set of all $2×2$ matrices with real entries such that all their eigenvalues belong to $C - R $, and $X = M_2(R)$. Is $U$ open?

Metrisability is hereditary property

Defining the $p$-adic metric on $\mathbb{Z}$

Continuous function from metric space to R

Prove that a length-minimizing path in a metric space is injective

Closed ball is a closed set

Let $p$ be a point in $X$ at which $f(p) \gt 0$ Show there is some positive number $r$ such that $f(q) \gt 0$ for all q in $B_r(p)$

Lipschitz functions form a Banach space, and Analyzing its Dual

About completing metric spaces

Rank Preserving Maps between Metric Spaces

A compact subset question

Consider $B\subset\Re^{n}$ a ball (open or closed). Show that for all $x\in B$, the set $B-\{x\}$ is connected.

To show a metric space is complete

Metric Topology: Collection of $B_d(x,\epsilon)$?

Diameter closure set

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