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 722 · Answer 1 · 2026-03-28 06:41:51

722

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 28 Mar 2026 - 6:41

score 363 · Answer 2 · 2018-03-31 13:02:29

363

Views

Metrisability is hereditary property

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score 133 · Answer 3 · 2026-03-25 07:41:53

133

Views

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

Published on 25 Mar 2026 - 7:41

score 176 · Answer 4 · 2026-03-25 03:17:13

176

Views

Continuous function from metric space to R

Published on 25 Mar 2026 - 3:17

score 136 · Answer 5 · 2026-03-25 01:17:00

136

Views

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

Published on 25 Mar 2026 - 1:17

score 583 · Answer 6 · 2018-04-01 21:32:56

583

Views

Closed ball is a closed set

Published on 01 Apr 2018 - 21:32

score 32 · Answer 7 · 2026-03-25 04:59:33

32

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 25 Mar 2026 - 4:59

score 1k · Answer 8 · 2026-03-25 00:24:27

1k

Views

Lipschitz functions form a Banach space, and Analyzing its Dual

Published on 25 Mar 2026 - 0:24

score 73 · Answer 9 · 2018-04-02 14:44:17

73

Views

About completing metric spaces

Published on 02 Apr 2018 - 14:44

score 58 · Answer 10 · 2026-03-24 23:43:05

58

Views

Rank Preserving Maps between Metric Spaces

Published on 24 Mar 2026 - 23:43

score 37 · Answer 11 · 2018-04-03 10:10:54

37

Views

A compact subset question

Published on 03 Apr 2018 - 10:10

score 47 · Answer 12 · 2026-03-25 18:08:26

47

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 25 Mar 2026 - 18:08

score 175 · Answer 13 · 2018-04-03 23:52:18

175

Views

To show a metric space is complete

Published on 03 Apr 2018 - 23:52

score 97 · Answer 14 · 2018-04-04 00:29:36

97

Views

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

Published on 04 Apr 2018 - 0:29

score 182 · Answer 15 · 2018-04-04 11:12:57

182

Views

Diameter closure set

Published on 04 Apr 2018 - 11:12

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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