Question

Let $(X,d)$ be a metric space, let $x\in X$, let $\delta <\epsilon$. Then, $\overline{B(x, \delta)} \subset B(x,\epsilon)$.

score 193 · Answer 1 · 2026-04-16 07:57:45

193

Views

Let $(X,d)$ be a metric space, let $x\in X$, let $\delta <\epsilon$. Then, $\overline{B(x, \delta)} \subset B(x,\epsilon)$.

Published on 16 Apr 2026 - 7:57

score 81 · Answer 2 · 2026-04-09 08:41:03

81

Views

Can't follow Proof in Folland: Outer Measures and Pre-measures.

Published on 09 Apr 2026 - 8:41

score 52 · Answer 3 · 2026-04-12 08:22:25

52

Views

Then $K$ is a) compact b) not compact?

Published on 12 Apr 2026 - 8:22

score 937 · Answer 4 · 2026-04-10 23:27:52

937

Views

Understanding the Product Topology

Published on 10 Apr 2026 - 23:27

score 124 · Answer 5 · 2026-04-08 18:18:32

Under which conditions a non-compact and connected space possesses a non-constant continuous real-valued function

score 100 · Answer 6 · 2026-04-16 09:24:23

100

Views

Let $\tau$ be lower limit topology on $\mathbb R.$ Then $(X,\tau)$ is not second countable.

Published on 16 Apr 2026 - 9:24

score 59 · Answer 7 · 2026-04-13 11:01:53

59

Views

Why the argument given by bof is not working for usual topology on $\mathbb R$?

Published on 13 Apr 2026 - 11:01

score 178 · Answer 8 · 2026-04-10 15:22:09

178

Views

Can a continuous bijection on the quotient space fail to be a homeomorphism?

Published on 10 Apr 2026 - 15:22

score 38 · Answer 9 · 2026-04-13 20:05:39

38

Views

Prove that $A=\{y\in M:d(x, y)\le r\}$ is closed in $M$

Published on 13 Apr 2026 - 20:05

score 224 · Answer 10 · 2026-04-14 19:29:15

224

Views

Proper maps between pairs

Published on 14 Apr 2026 - 19:29

score 62 · Answer 11 · 2026-04-14 20:45:04

62

Views

Removing points of discontinuity

Published on 14 Apr 2026 - 20:45

score 33 · Answer 12 · 2026-04-16 14:57:41

33

Views

Looping properties of recursive chains of a special type of boundary of a set

Published on 16 Apr 2026 - 14:57

score 66 · Answer 13 · 2026-04-10 03:45:18

66

Views

Basic analysis/topology of a sequence proof

Published on 10 Apr 2026 - 3:45

score 412 · Answer 14 · 2026-04-10 11:36:05

412

Views

What does it mean for a (non-smooth) homeomorphism between oriented smooth manifolds to be orientation preserving?

Published on 10 Apr 2026 - 11:36

score 788 · Answer 15 · 2026-04-09 00:49:20

788

Views

Induced homomorphism between fundamental groups

Published on 09 Apr 2026 - 0:49

List Question

Let $(X,d)$ be a metric space, let $x\in X$, let $\delta <\epsilon$. Then, $\overline{B(x, \delta)} \subset B(x,\epsilon)$.

Can't follow Proof in Folland: Outer Measures and Pre-measures.

Then $K$ is a) compact b) not compact?

Understanding the Product Topology

Under which conditions a non-compact and connected space possesses a non-constant continuous real-valued function

Let $\tau$ be lower limit topology on $\mathbb R.$ Then $(X,\tau)$ is not second countable.

Why the argument given by bof is not working for usual topology on $\mathbb R$?

Can a continuous bijection on the quotient space fail to be a homeomorphism?

Prove that $A=\{y\in M:d(x, y)\le r\}$ is closed in $M$

Proper maps between pairs

Removing points of discontinuity

Looping properties of recursive chains of a special type of boundary of a set

Basic analysis/topology of a sequence proof

What does it mean for a (non-smooth) homeomorphism between oriented smooth manifolds to be orientation preserving?

Induced homomorphism between fundamental groups

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