Question

Please clarify proof that $\mathbb R_K$ is not path connected.

score 2.9k · Answer 1 · 2026-04-09 17:24:21

2.9k

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Please clarify proof that $\mathbb R_K$ is not path connected.

Published on 09 Apr 2026 - 17:24

score 51 · Answer 2 · 2026-04-12 19:06:15

51

Views

A reflection map in the class of compact spaces is an embedding

Published on 12 Apr 2026 - 19:06

score 20 · Answer 3 · 2026-04-14 12:02:04

20

Views

Find/Prove Compact Subspace that is Non-Closed

Published on 14 Apr 2026 - 12:02

score 362 · Answer 4 · 2026-04-11 11:14:20

362

Views

Pointwise convergence of average of continuous functions

Published on 11 Apr 2026 - 11:14

score 334 · Answer 5 · 2026-04-16 10:38:10

Family of Compact Sets as subset of $X$ wherein the finite intersection is non-empty, implies the infinite intersection is non-empty

score 197 · Answer 6 · 2026-04-11 02:26:04

197

Views

Problem 24. Introduction to Hilbert spaces. Stein

Published on 11 Apr 2026 - 2:26

score 336 · Answer 7 · 2026-04-17 10:53:36

336

Views

If for every linear mapping image of convex set is compact then this set is compact

Published on 17 Apr 2026 - 10:53

score 1.2k · Answer 8 · 2026-04-13 21:53:04

1.2k

Views

When is a proper map closed?

Published on 13 Apr 2026 - 21:53

score 247 · Answer 9 · 2026-05-11 05:43:26

247

Views

If (X,d) is a metric space and $K \subseteq X$ is compact. Show that $K$ is complete.

Published on 11 May 2026 - 5:43

score 304 · Answer 10 · 2026-04-14 20:31:46

304

Views

GRE 0568 #65: Disprove 'There is a continuous one-to-one function from $(0,1)$ onto $[0,1].$'

Published on 14 Apr 2026 - 20:31

score 44 · Answer 11 · 2026-04-11 06:24:22

44

Views

Is a topology, generated by intersections of opens from two compact topologies, itself compact?

Published on 11 Apr 2026 - 6:24

score 431 · Answer 12 · 2026-05-10 16:13:57

431

Views

GRE 9367 #62: Prove $X=[0,1]$ in lower limit topology ($[a,b)$) is not compact, is Hausdorff and is disconnected.

Published on 10 May 2026 - 16:13

score 504 · Answer 13 · 2026-04-13 21:05:05

504

Views

Nested sequence of compact subsets covering an open set in $\mathbb{R}^n$

Published on 13 Apr 2026 - 21:05

score 198 · Answer 14 · 2026-04-17 03:29:48

198

Views

About the total boundedness of a given set in a complete Metric Space

Published on 17 Apr 2026 - 3:29

score 600 · Answer 15 · 2026-05-10 17:15:48

600

Views

What are some other topological invariants apart from connectedness, compactness and fundamental groups?

Published on 10 May 2026 - 17:15

List Question

Please clarify proof that $\mathbb R_K$ is not path connected.

A reflection map in the class of compact spaces is an embedding

Find/Prove Compact Subspace that is Non-Closed

Pointwise convergence of average of continuous functions

Family of Compact Sets as subset of $X$ wherein the finite intersection is non-empty, implies the infinite intersection is non-empty

Problem 24. Introduction to Hilbert spaces. Stein

If for every linear mapping image of convex set is compact then this set is compact

When is a proper map closed?

If (X,d) is a metric space and $K \subseteq X$ is compact. Show that $K$ is complete.

GRE 0568 #65: Disprove 'There is a continuous one-to-one function from $(0,1)$ onto $[0,1].$'

Is a topology, generated by intersections of opens from two compact topologies, itself compact?

GRE 9367 #62: Prove $X=[0,1]$ in lower limit topology ($[a,b)$) is not compact, is Hausdorff and is disconnected.

Nested sequence of compact subsets covering an open set in $\mathbb{R}^n$

About the total boundedness of a given set in a complete Metric Space

What are some other topological invariants apart from connectedness, compactness and fundamental groups?

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