Topic: Counterexamples in Topology

Why The Sorgenfrey Line Is Separable But Not Second Countable

Why The Long Line Is Not Metrizable

Uncountably Many Loop Classes In The Hawaiian Earring

The Topologist’s Sine Curve As A Connected Closure

The Sierpinski Space As An Open-Set Classifier

The Lower Limit Topology And Half-Open Basis Intervals

The Long Line And Its Local Euclidean Structure

The Hawaiian Earring Is Not Semilocally Simply Connected

The Cantor Set As A Perfect Nowhere-Dense Compactum

Nonunique Limits In The Sierpinski Space