Topic: Continuous Maps and Homeomorphisms

The Subbasis Criterion for Continuity

The Open-Cover Pasting Lemma

The Closed-Set Test for Continuity

The Closed-Cover Pasting Lemma

The Basis Criterion for Continuity

Testing Open Maps on a Basis

Properties Preserved by Homeomorphisms

Piecewise Maps on Real Intervals

Open Maps and Their Images

Open Bijections and Closed Bijections