Question

Assume a real-valued net has a cluster point $a\in \mathbb R$. Is there a cofinal subnet converging to $a$?

score 162 · Answer 1 · 2021-02-16 18:51:21

162

Views

Assume a real-valued net has a cluster point $a\in \mathbb R$. Is there a cofinal subnet converging to $a$?

Published on 16 Feb 2021 - 18:51

score 163 · Answer 2 · 2021-02-21 16:08:11

163

Views

Proving uncountable sum as series using nets.

Published on 21 Feb 2021 - 16:08

score 28 · Answer 3 · 2021-03-02 05:09:10

28

Views

Question about terminology regarding nets

Published on 02 Mar 2021 - 5:09

score 46 · Answer 4 · 2021-03-06 14:17:26

$N(X)$ denotes collection of all nets of $X$. $T:N(X)\to \mathcal{P}(X)$ be a map such that $T\{x_\delta\}=T\{y_\gamma\}$ if one is subnet of other.

score 105 · Answer 5 · 2021-03-09 08:01:37

105

Views

Is intersection of a subset with a net a subnet?

Published on 09 Mar 2021 - 8:01

score 66 · Answer 6 · 2021-03-19 15:31:37

Let $(a_d)_{d\in D}$ be a real net such that $\lim_{d\in D}a_d=∞$. Is there a cofinal set $D'\subset D$ such that $(a_d)_{d\in D'}$ is increasing?

score 95 · Answer 7 · 2021-03-20 02:13:56

95

Views

How does one show that if $B \subset A$ (where $A$ is a directed set) is cofinal in $(A, \leq)$ then $(B, \leq)$ is a directed set?

Published on 20 Mar 2021 - 2:13

score 65 · Answer 8 · 2021-04-06 12:30:51

65

Views

Construction of a net and the usage of Axiom of Choice

Published on 06 Apr 2021 - 12:30

score 31 · Answer 9 · 2021-04-09 08:58:25

31

Views

Does the concept of a positive null net make sense for all directed sets?

Published on 09 Apr 2021 - 8:58

score 245 · Answer 10 · 2021-04-10 11:33:57

245

Views

Ex.11 Sec.I-4 Conway's Functional Analysis

Published on 10 Apr 2021 - 11:33

score 284 · Answer 11 · 2021-04-10 12:52:49

284

Views

Topology axioms in terms of net convergence

Published on 10 Apr 2021 - 12:52

score 78 · Answer 12 · 2021-04-11 14:19:44

78

Views

Nets: frequently in $A$ iff eventually not in $X\setminus A$?

Published on 11 Apr 2021 - 14:19

score 40 · Answer 13 · 2021-04-17 04:12:02

40

Views

Negation statement a net

Published on 17 Apr 2021 - 4:12

score 90 · Answer 14 · 2021-05-03 10:00:03

90

Views

How to define a topology with a given convergence of nets.

Published on 03 May 2021 - 10:00

score 282 · Answer 15 · 2021-05-11 18:29:38

282

Views

Example of an unbounded convergent net in a metric space

Published on 11 May 2021 - 18:29

List Question

Assume a real-valued net has a cluster point $a\in \mathbb R$. Is there a cofinal subnet converging to $a$?

Proving uncountable sum as series using nets.

Question about terminology regarding nets

$N(X)$ denotes collection of all nets of $X$. $T:N(X)\to \mathcal{P}(X)$ be a map such that $T\{x_\delta\}=T\{y_\gamma\}$ if one is subnet of other.

Is intersection of a subset with a net a subnet?

Let $(a_d)_{d\in D}$ be a real net such that $\lim_{d\in D}a_d=∞$. Is there a cofinal set $D'\subset D$ such that $(a_d)_{d\in D'}$ is increasing?

How does one show that if $B \subset A$ (where $A$ is a directed set) is cofinal in $(A, \leq)$ then $(B, \leq)$ is a directed set?

Construction of a net and the usage of Axiom of Choice

Does the concept of a positive null net make sense for all directed sets?

Ex.11 Sec.I-4 Conway's Functional Analysis

Topology axioms in terms of net convergence

Nets: frequently in $A$ iff eventually not in $X\setminus A$?

Negation statement a net

How to define a topology with a given convergence of nets.

Example of an unbounded convergent net in a metric space

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