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Second-countable
New post in Second-countable
$\mathbb{R}^n$ Second Countable
August 1st, 2022
proof-writing
general-topology
second-countable
manifolds
solution-verification
Confusion regarding the proof to "every Lindelöf metric space is second countable".
October 9th, 2020
lindelof-spaces
second-countable
general-topology
Prove that $\mathbb{R}_l$ is not a second countable. ($\mathbb{R}_l$ are the real ones with the topology of the lower limit)
November 27th, 2020
second-countable
general-topology
analysis
Compact metrizable space has a countable basis (Munkres Topology)
December 28th, 2020
second-countable
general-topology
metric-spaces
compactness
If $(X, \mathcal{T})$ has a countable subbasis, then it has a countable basis
December 29th, 2020
general-topology
second-countable
cardinals
proof-verification
Does there exist a Connected Locally Euclidean Space that is not second countable?
August 1st, 2022
examples-counterexamples
connectedness
second-countable
general-topology
Is a separable and metrizable space second countable?
August 1st, 2022
second-countable
metric-spaces
general-topology
separable-spaces
locally compact Hausdorff space which is not second-countable
August 1st, 2022
second-countable
examples-counterexamples
compactness
general-topology
Second Countable, First Countable, and Separable Spaces
August 1st, 2022
second-countable
separable-spaces
first-countable
general-topology
Why must a locally compact second countable Hausdorff space be second countable to imply paracompactness?
August 1st, 2022
compactness
general-topology
examples-counterexamples
second-countable
First countable + separable imply second countable?
August 1st, 2022
separable-spaces
general-topology
second-countable
first-countable
examples-counterexamples
Separable implies second countable
May 21st, 2020
separable-spaces
general-topology
second-countable
Compact metric spaces is second countable and axiom of countable choice
August 1st, 2022
set-theory
general-topology
compactness
axiom-of-choice
second-countable
Every locally compact, second countable Hausdorff space has a countable basis of open sets with compact closure
August 1st, 2022
second-countable
general-topology
When is the quotient space of a second countable space second countable?
August 1st, 2022
general-topology
quotient-spaces
open-map
second-countable
examples-counterexamples
Equivalence of three properties of a metric space.
August 1st, 2022
general-topology
separable-spaces
second-countable
metric-spaces
Hausdorff locally compact and second countable is $\sigma$-compact
August 1st, 2022
general-topology
second-countable
Compact topological space not having Countable Basis?
August 1st, 2022
compactness
product-space
general-topology
second-countable
examples-counterexamples
Does proving (second countable) $\Rightarrow$ (Lindelöf) require the axiom of choice?
August 1st, 2022
set-theory
general-topology
axiom-of-choice
second-countable
If X is second-countable, then X is Lindelöf.
August 1st, 2022
second-countable
general-topology
proof-explanation
Every separable metric space has a countable base
August 1st, 2022
solution-verification
metric-spaces
separable-spaces
general-topology
second-countable
Second-countable implies separable/Axiom countable choice
August 1st, 2022
separable-spaces
second-countable
general-topology
axiom-of-choice
elementary-set-theory
Show that every compact metrizable space has a countable basis
August 1st, 2022
compactness
general-topology
proof-verification
metric-spaces
second-countable
A metric space is separable iff it is second countable
August 1st, 2022
metric-spaces
general-topology
separable-spaces
second-countable
When is $C_0(X)$ separable?
August 1st, 2022
functional-analysis
general-topology
separable-spaces
separation-axioms
second-countable
An uncountable set in a second countable space has limit points.
March 26th, 2020
second-countable
general-topology
Lindelöf and second countable spaces
August 1st, 2022
real-analysis
general-topology
second-countable
lindelof-spaces
Is one-point compactification of a space metrizable
August 1st, 2022
general-topology
second-countable
metric-spaces
compactness
compactification