Question

Can we say anything about the set of all points of discontinuities of $f^{(1)}$,the derivative of a differentiable function on $\mathbb R$.

score 23 · Answer 1 · 2019-12-27 05:15:00

23

Views

Can we say anything about the set of all points of discontinuities of $f^{(1)}$,the derivative of a differentiable function on $\mathbb R$.

Published on 27 Dec 2019 - 5:15

score 224 · Answer 2 · 2019-12-29 00:26:31

224

Views

Sequence of unbounded continuous functions

Published on 29 Dec 2019 - 0:26

score 90 · Answer 3 · 2020-01-03 16:31:14

90

Views

Given a normed vector space, prove that a dense subspace, that is also $G_\delta$ is the entire space.

Published on 03 Jan 2020 - 16:31

score 159 · Answer 4 · 2020-01-05 20:18:25

159

Views

Remark in "Lecture Notes on Elementary Topology and Differential Geometry" (Singer/Thorpe)

Published on 05 Jan 2020 - 20:18

score 109 · Answer 5 · 2020-01-07 09:40:20

109

Views

Precision on the Baire category theorem

Published on 07 Jan 2020 - 9:40

score 71 · Answer 6 · 2020-01-15 15:49:43

71

Views

Is a comeagre set closed

Published on 15 Jan 2020 - 15:49

score 174 · Answer 7 · 2020-01-22 20:47:27

174

Views

Pseudocomplete spaces

Published on 22 Jan 2020 - 20:47

score 493 · Answer 8 · 2020-02-12 12:30:48

493

Views

Counterexample to the Converse of Baire's Category Theorem

Published on 12 Feb 2020 - 12:30

score 125 · Answer 9 · 2026-03-26 12:35:22

125

Views

Equivalence of Baire Theorem

Published on 26 Mar 2026 - 12:35

score 96 · Answer 10 · 2026-03-25 09:50:04

96

Views

Can $X \setminus Y$ be first category? For $Y$ a proper linear subspace of a completely metrizable TVS $X$

Published on 25 Mar 2026 - 9:50

score 34 · Answer 11 · 2020-03-07 05:46:34

34

Views

Can a dense set $X$ in $\mathbb R$ contain a proper subset $A$ such that $A$ and $X-A$ are not dense in $\mathbb R$?

Published on 07 Mar 2020 - 5:46

score 115 · Answer 12 · 2020-03-16 14:54:56

115

Views

Proof attempt of Baire's Category theorem.

Published on 16 Mar 2020 - 14:54

score 447 · Answer 13 · 2020-03-17 04:24:11

447

Views

Meagre sets have empty interior-A false statement.

Published on 17 Mar 2020 - 4:24

score 834 · Answer 14 · 2020-03-18 03:38:23

834

Views

In a complete metric space,first category sets are 'meagre' in the sense that they cannot contain any non-empty open set.

Published on 18 Mar 2020 - 3:38

score 96 · Answer 15 · 2020-03-18 05:13:43

96

Views

Mixing category and measure

Published on 18 Mar 2020 - 5:13

List Question

Can we say anything about the set of all points of discontinuities of $f^{(1)}$,the derivative of a differentiable function on $\mathbb R$.

Sequence of unbounded continuous functions

Given a normed vector space, prove that a dense subspace, that is also $G_\delta$ is the entire space.

Remark in "Lecture Notes on Elementary Topology and Differential Geometry" (Singer/Thorpe)

Precision on the Baire category theorem

Is a comeagre set closed

Pseudocomplete spaces

Counterexample to the Converse of Baire's Category Theorem

Equivalence of Baire Theorem

Can $X \setminus Y$ be first category? For $Y$ a proper linear subspace of a completely metrizable TVS $X$

Can a dense set $X$ in $\mathbb R$ contain a proper subset $A$ such that $A$ and $X-A$ are not dense in $\mathbb R$?

Proof attempt of Baire's Category theorem.

Meagre sets have empty interior-A false statement.

In a complete metric space,first category sets are 'meagre' in the sense that they cannot contain any non-empty open set.

Mixing category and measure

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