Question

General topology / real analysis - Suppose $S$ is a bounded and closed nonempty subset of real numbers. Prove sup S is in S

score 286 · Answer 1 · 2026-04-13 09:58:58

286

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General topology / real analysis - Suppose $S$ is a bounded and closed nonempty subset of real numbers. Prove sup S is in S

Published on 13 Apr 2026 - 9:58

score 217 · Answer 2 · 2026-04-12 19:30:31

217

Views

Is the problem VIII, 1.6 of Dungundji's Topology right?

Published on 12 Apr 2026 - 19:30

score 134 · Answer 3 · 2026-04-15 03:16:51

134

Views

Inverse of a cycloid

Published on 15 Apr 2026 - 3:16

score 64 · Answer 4 · 2026-04-21 11:56:00

64

Views

how should one picture a topological space

Published on 21 Apr 2026 - 11:56

score 678 · Answer 5 · 2026-04-18 04:28:59

678

Views

Let $f$ be a continuous function such that $f(f(x))=x$

Published on 18 Apr 2026 - 4:28

score 378 · Answer 6 · 2026-04-14 05:12:22

378

Views

Every open set is a continuous image of closed set

Published on 14 Apr 2026 - 5:12

score 907 · Answer 7 · 2026-04-12 20:52:47

907

Views

About the concept of locally finite topological space

Published on 12 Apr 2026 - 20:52

score 857 · Answer 8 · 2026-04-15 07:16:33

857

Views

How to show if there exists a global frame for a vector bundle, then the vector bundle is trivial.

Published on 15 Apr 2026 - 7:16

score 464 · Answer 9 · 2026-04-11 22:51:06

Compact convergence and compact-open topologies on $\mathcal{C}(X,Y)$ coincide when $Y$ is metric [Proof Verification]

score 231 · Answer 10 · 2026-04-14 05:07:31

231

Views

A locally finite topological space is Alexandrov

Published on 14 Apr 2026 - 5:07

score 62 · Answer 11 · 2026-04-14 01:34:47

62

Views

What does it mean that embedding inherit same topology? Banach-Alaoglu

Published on 14 Apr 2026 - 1:34

score 138 · Answer 12 · 2026-04-14 07:51:48

138

Views

Intuitively, how is the proof of IVT with connectedness equivalent to the proof with completeness?

Published on 14 Apr 2026 - 7:51

score 102 · Answer 13 · 2026-04-12 08:51:35

102

Views

Is the union of disjoint, non-Borel sets also non-Borel?

Published on 12 Apr 2026 - 8:51

score 35 · Answer 14 · 2026-04-11 08:23:32

35

Views

Does Descartes' theorem work for non-convex polyhedrons?

Published on 11 Apr 2026 - 8:23

score 71 · Answer 15 · 2026-04-16 11:58:38

Prove that $A=\{x\in X:$ there is a simple chain consisting of members of $\mathscr O$ that connects $a$ and $x\}$ is open

List Question

General topology / real analysis - Suppose $S$ is a bounded and closed nonempty subset of real numbers. Prove sup S is in S

Is the problem VIII, 1.6 of Dungundji's Topology right?

Inverse of a cycloid

how should one picture a topological space

Let $f$ be a continuous function such that $f(f(x))=x$

Every open set is a continuous image of closed set

About the concept of locally finite topological space

How to show if there exists a global frame for a vector bundle, then the vector bundle is trivial.

Compact convergence and compact-open topologies on $\mathcal{C}(X,Y)$ coincide when $Y$ is metric [Proof Verification]

A locally finite topological space is Alexandrov

What does it mean that embedding inherit same topology? Banach-Alaoglu

Intuitively, how is the proof of IVT with connectedness equivalent to the proof with completeness?

Is the union of disjoint, non-Borel sets also non-Borel?

Does Descartes' theorem work for non-convex polyhedrons?

Prove that $A=\{x\in X:$ there is a simple chain consisting of members of $\mathscr O$ that connects $a$ and $x\}$ is open

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