Question

How many connected components for the intersection $S \cap GL_n(\mathbb R)$ where $S \subset M_n(\mathbb R)$ is a linear subspace?

score 139 · Answer 1 · 2018-07-21 06:02:13

139

Views

How many connected components for the intersection $S \cap GL_n(\mathbb R)$ where $S \subset M_n(\mathbb R)$ is a linear subspace?

Published on 21 Jul 2018 - 6:02

score 257 · Answer 2 · 2018-07-22 00:37:08

257

Views

When does $S \cap GL_4(\mathbb R)$ have precisely two connected components where $S \subset M_4(\mathbb R)$ is a linear subspace?

Published on 22 Jul 2018 - 0:37

score 49 · Answer 3 · 2018-07-22 06:04:41

49

Views

Why this argument does not make sense on connected components of $GL_n(\mathbb R)$?

Published on 22 Jul 2018 - 6:04

score 1.4k · Answer 4 · 2018-07-23 15:02:44

1.4k

Views

about $C([0,1])$ with sup metric

Published on 23 Jul 2018 - 15:02

score 134 · Answer 5 · 2018-07-23 16:46:04

134

Views

Is R is connected subspace of R2.?

Published on 23 Jul 2018 - 16:46

score 106 · Answer 6 · 2018-07-25 17:07:44

106

Views

Given $X \subset \mathbb{R}^{n}$ connected, if $A \subset X$ is such that $\partial A \cap X = \emptyset$, then $A = \emptyset$ or $A=X$

Published on 25 Jul 2018 - 17:07

score 482 · Answer 7 · 2018-07-26 01:52:47

482

Views

Connected components of real matrices in $M_n(\mathbb R)$ with constant rank $k$

Published on 26 Jul 2018 - 1:52

score 649 · Answer 8 · 2026-03-25 11:16:34

649

Views

Prob. 1, Sec. 25, in Munkres' TOPOLOGY, 2nd ed: The components and the path components of $\mathbb{R}$ with lower limit topology

Published on 25 Mar 2026 - 11:16

score 425 · Answer 9 · 2026-03-25 11:16:41

425

Views

Prob. 2(b), Sec. 25, in Munkres' TOPOLOGY, 2nd ed: The iff-condition for two points to be in the same component of $\mathbb{R}^\omega$

Published on 25 Mar 2026 - 11:16

score 281 · Answer 10 · 2018-07-29 11:34:11

281

Views

Elementary topology of $\mathbb C$: Union of 2 regions with nonempty intersection is a region

Published on 29 Jul 2018 - 11:34

score 139 · Answer 11 · 2026-03-25 06:00:03

139

Views

Difference Between Zero-Dimensional and Totally Separated in the Plane

Published on 25 Mar 2026 - 6:00

score 1.1k · Answer 12 · 2018-07-30 10:36:35

1.1k

Views

Sketch the sets in $\mathbb C$ and determine whether they are open, closed, or neither; bounded; connected and their boundaries.

Published on 30 Jul 2018 - 10:36

score 569 · Answer 13 · 2026-03-25 15:58:59

569

Views

Connecting points in an annulus with horizontal and vertical segments

Published on 25 Mar 2026 - 15:58

score 374 · Answer 14 · 2018-07-31 04:55:00

374

Views

Properties of a Set Consisting of a Single Point

Published on 31 Jul 2018 - 4:55

score 358 · Answer 15 · 2026-03-25 16:03:14

358

Views

Do locally path connected locally compact metric spaces have an intrinsic metric?

Published on 25 Mar 2026 - 16:03

List Question

How many connected components for the intersection $S \cap GL_n(\mathbb R)$ where $S \subset M_n(\mathbb R)$ is a linear subspace?

When does $S \cap GL_4(\mathbb R)$ have precisely two connected components where $S \subset M_4(\mathbb R)$ is a linear subspace?

Why this argument does not make sense on connected components of $GL_n(\mathbb R)$?

about $C([0,1])$ with sup metric

Is R is connected subspace of R2.?

Given $X \subset \mathbb{R}^{n}$ connected, if $A \subset X$ is such that $\partial A \cap X = \emptyset$, then $A = \emptyset$ or $A=X$

Connected components of real matrices in $M_n(\mathbb R)$ with constant rank $k$

Prob. 1, Sec. 25, in Munkres' TOPOLOGY, 2nd ed: The components and the path components of $\mathbb{R}$ with lower limit topology

Prob. 2(b), Sec. 25, in Munkres' TOPOLOGY, 2nd ed: The iff-condition for two points to be in the same component of $\mathbb{R}^\omega$

Elementary topology of $\mathbb C$: Union of 2 regions with nonempty intersection is a region

Difference Between Zero-Dimensional and Totally Separated in the Plane

Sketch the sets in $\mathbb C$ and determine whether they are open, closed, or neither; bounded; connected and their boundaries.

Connecting points in an annulus with horizontal and vertical segments

Properties of a Set Consisting of a Single Point

Do locally path connected locally compact metric spaces have an intrinsic metric?

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