Question

Is a set of circles in $\mathbb{R}^2$ such that no two circles (not discs) overlap necessarily countable or possibly uncountable?

score 486 · Answer 1 · 2017-07-06 06:11:33

486

Views

Is a set of circles in $\mathbb{R}^2$ such that no two circles (not discs) overlap necessarily countable or possibly uncountable?

Published on 06 Jul 2017 - 6:11

score 455 · Answer 2 · 2017-08-01 22:19:27

455

Views

Prove that a countably compact, first countable $T_{2}$ space is regular.

Published on 01 Aug 2017 - 22:19

score 249 · Answer 3 · 2017-08-11 00:30:57

249

Views

Show that a sequence in $X$ converges $⇔$ it has a single cluster point

Published on 11 Aug 2017 - 0:30

score 758 · Answer 4 · 2017-10-08 04:28:32

758

Views

Prob. 4, Sec. 21, in Munkres' TOPOLOGY, 2nd ed: First countability of $\mathbb{R}_l$ and of the ordered square

Published on 08 Oct 2017 - 4:28

score 50 · Answer 5 · 2017-10-15 20:53:59

50

Views

Infinite Sets (1st yr Uni) and Axioms

Published on 15 Oct 2017 - 20:53

score 357 · Answer 6 · 2017-10-20 11:34:53

357

Views

How many real function are there?

Published on 20 Oct 2017 - 11:34

score 133 · Answer 7 · 2017-12-26 10:39:53

133

Views

Each $C^*$-embedded subset $S$ of a first countable Tychonoff space $X$ is closed.

Published on 26 Dec 2017 - 10:39

score 106 · Answer 8 · 2018-01-09 00:33:59

106

Views

First-order topologies, limit-points and convergent sequences

Published on 09 Jan 2018 - 0:33

score 3.7k · Answer 9 · 2011-09-18 04:09:54

3.7k

Views

Bases having countable subfamilies which are bases in second countable space

Published on 18 Sep 2011 - 4:09

score 2.7k · Answer 10 · 2011-09-25 23:27:55

2.7k

Views

Uncountable Cartesian product of closed interval

Published on 25 Sep 2011 - 23:27

score 53 · Answer 11 · 2020-07-31 17:22:30

53

Views

Problem with extension of a continous function

Published on 31 Jul 2020 - 17:22

score 119 · Answer 12 · 2020-08-01 15:18:33

119

Views

Is a locally compact Hausdorff quotient of a locally compact $\sigma$-compact first countable Hausdorff space always first countable?

Published on 01 Aug 2020 - 15:18

score 118 · Answer 13 · 2020-08-01 18:45:34

118

Views

Is a locally compact Hausdorff quotient of a locally compact $\sigma$-compact first countable Hausdorff space always Frechet-Urysohn?

Published on 01 Aug 2020 - 18:45

score 81 · Answer 14 · 2020-08-03 19:11:08

81

Views

Is a locally compact Hausdorff quotient of a locally compact $\sigma$-compact first countable Hausdorff space first countable on a dense set?

Published on 03 Aug 2020 - 19:11

score 273 · Answer 15 · 2026-02-23 05:12:20

273

Views

Is a locally compact hereditarily Lindelof Hausdorff space first countable?

Published on 23 Feb 2026 - 5:12

List Question

Is a set of circles in $\mathbb{R}^2$ such that no two circles (not discs) overlap necessarily countable or possibly uncountable?

Prove that a countably compact, first countable $T_{2}$ space is regular.

Show that a sequence in $X$ converges $⇔$ it has a single cluster point

Prob. 4, Sec. 21, in Munkres' TOPOLOGY, 2nd ed: First countability of $\mathbb{R}_l$ and of the ordered square

Infinite Sets (1st yr Uni) and Axioms

How many real function are there?

Each $C^*$-embedded subset $S$ of a first countable Tychonoff space $X$ is closed.

First-order topologies, limit-points and convergent sequences

Bases having countable subfamilies which are bases in second countable space

Uncountable Cartesian product of closed interval

Problem with extension of a continous function

Is a locally compact Hausdorff quotient of a locally compact $\sigma$-compact first countable Hausdorff space always first countable?

Is a locally compact Hausdorff quotient of a locally compact $\sigma$-compact first countable Hausdorff space always Frechet-Urysohn?

Is a locally compact Hausdorff quotient of a locally compact $\sigma$-compact first countable Hausdorff space first countable on a dense set?

Is a locally compact hereditarily Lindelof Hausdorff space first countable?

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