Topic: Topology (Undergraduate)

The Basis Criterion for Continuity

The Basis Criterion for Product Rectangles

The Banach Fixed-Point Theorem

The Basis Criterion for Collections of Subsets

The Antipodal Difference Map for Borsuk-Ulam

The Axioms Defining a Topology

Testing Whether a Retraction Is a Deformation Retraction

Testing Topology Inclusions with Open Sets

Testing Metrizability with Base Criteria

Testing Open Maps on a Basis