Each countable base of a topology contains countable subfamily which is also a base
33207
Bases having countable subfamilies which are bases in second countable space
140799
Prove that there exist uncountable family of subsets of $\mathbb{N}$ which is linearly (totally) ordered by relation of inclusion.
62793
$\mathbb{R}$ with the lower limit topology is not second-countable
48174
Are countable topological spaces second-countable?
40937
Is the set of partial order relations over $ \mathbb{N}$ countable?
88028
Topology - closures of intervals with the order topology
92526
Collection of clopen sets form a base for a countable completely regular space
44623
Closed set as a countable intersection of open sets
7723
Countable basis of function spaces
137621
The Number of Topologies on a Finite Set
82989
T4 and first countable topology that is non metrizable
70143
Mutually exclusive countable subsets of a countable set
3708
How can I prove that compact subset iff sequentially compact in second countable topological spaces?
70048
In which topologies do open sets maintain open under countable or arbitrary intersection?
105358
In a second countable space any base has a countable subset that is still a base
81509
The cardinality of a countable union of countable sets, without the axiom of choice
101986
Prob. 2, Sec. 20 in Munkres' TOPOLOGY, 2nd ed: The dictionary order topology on $\mathbb{R} \times \mathbb{R}$ is metrizable.