Question

Proof that if $f:S^{n} \to \mathbb{R} $ is continuous, then is not injective

score 227 · Answer 1 · 2018-06-07 16:27:11

227

Views

Proof that if $f:S^{n} \to \mathbb{R} $ is continuous, then is not injective

Published on 07 Jun 2018 - 16:27

score 33 · Answer 2 · 2026-03-25 09:53:30

33

Views

Path connectedness of a subset of $R^2$

Published on 25 Mar 2026 - 9:53

score 126 · Answer 3 · 2026-03-25 09:49:28

126

Views

Which of the following spaces are connected?

Published on 25 Mar 2026 - 9:49

score 77 · Answer 4 · 2026-03-25 11:20:19

77

Views

Is the preimage of $f\colon (x_1, x_2) \mapsto x_1+x_2 +x_1x_2$ connected?

Published on 25 Mar 2026 - 11:20

score 235 · Answer 5 · 2018-06-08 18:30:28

235

Views

Connectedness of a subset of structured matrices satisfying prescribed conditions on roots of polynomials

Published on 08 Jun 2018 - 18:30

score 398 · Answer 6 · 2026-03-25 20:35:17

398

Views

Čech-Stone compactification of extremally disconnected space

Published on 25 Mar 2026 - 20:35

score 118 · Answer 7 · 2026-03-25 01:33:55

118

Views

Extremally disconnected implies $T_1$?

Published on 25 Mar 2026 - 1:33

score 411 · Answer 8 · 2026-03-25 09:53:26

411

Views

Path-connectedness of the boundary of a set?

Published on 25 Mar 2026 - 9:53

score 322 · Answer 9 · 2026-03-25 06:29:22

322

Views

Equivalence relation on topological space such that each equivalence class and the quotient space is connected

Published on 25 Mar 2026 - 6:29

score 300 · Answer 10 · 2018-06-18 20:45:01

300

Views

Do partitions of a square into two sets always connect one pair of opposite edges?

Published on 18 Jun 2018 - 20:45

score 474 · Answer 11 · 2018-06-20 18:22:22

What are the connected components of $\Bbb R^2 \setminus \big(\{(x,y) \in \Bbb R^2, x^2+y^2=1\} \cup \{(x,y)\in \Bbb R^2, y=x^2+1\}\big)$?

score 978 · Answer 12 · 2026-03-20 05:52:49

978

Views

Show that $CX$ is locally (path-)connected iff $X$ is

Published on 20 Mar 2026 - 5:52

score 137 · Answer 13 · 2026-03-25 09:48:19

137

Views

Countably Compact, Separable, $T_1$, Connected Space that is not Compact

Published on 25 Mar 2026 - 9:48

score 274 · Answer 14 · 2026-03-19 23:22:39

274

Views

Existence of Connected Sets in Complements of Closed Sets

Published on 19 Mar 2026 - 23:22

score 15 · Answer 15 · 2018-06-28 20:23:25

15

Views

Find the component of $y\in \prod_{\alpha}Y_{\alpha}$

Published on 28 Jun 2018 - 20:23

List Question

Proof that if $f:S^{n} \to \mathbb{R} $ is continuous, then is not injective

Path connectedness of a subset of $R^2$

Which of the following spaces are connected?

Is the preimage of $f\colon (x_1, x_2) \mapsto x_1+x_2 +x_1x_2$ connected?

Connectedness of a subset of structured matrices satisfying prescribed conditions on roots of polynomials

Čech-Stone compactification of extremally disconnected space

Extremally disconnected implies $T_1$?

Path-connectedness of the boundary of a set?

Equivalence relation on topological space such that each equivalence class and the quotient space is connected

Do partitions of a square into two sets always connect one pair of opposite edges?

What are the connected components of $\Bbb R^2 \setminus \big(\{(x,y) \in \Bbb R^2, x^2+y^2=1\} \cup \{(x,y)\in \Bbb R^2, y=x^2+1\}\big)$?

Show that $CX$ is locally (path-)connected iff $X$ is

Countably Compact, Separable, $T_1$, Connected Space that is not Compact

Existence of Connected Sets in Complements of Closed Sets

Find the component of $y\in \prod_{\alpha}Y_{\alpha}$

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