Topic: Countability Axioms and Sequences

The Uncountable Discrete Space As A Countability Counterexample

The Sorgenfrey Plane: Separable But Not Lindelof

The Sorgenfrey Line: Separable But Not Second Countable

The Cocountable Topology: Lindelof But Not Second Countable

Testing Continuity With Convergent Sequences

Sequential Continuity Without First Countability

Separable Spaces And Dense Countable Subsets

Separability And Second Countability In Metric Spaces

Separability Can Fail To Pass To Subspaces

Lindelof Spaces And Countable Subcovers