Topic: Urysohn's Lemma and the Tietze Extension Theorem

Metric Distance Functions as Separation Tools

Finite Partitions of Unity from Urysohn Functions

Dyadic Rationals for Urysohn’s Construction

Defining the Urysohn Function by Dyadic Infima

Coordinatewise Extension of Euclidean-Valued Maps

Continuous Separation of Disjoint Closed Sets

Continuous Bump Functions Around Closed Sets

Complete Regularity via Point-Closed Set Separation

Complete Regularity, Normality, and Tychonoff Spaces

Common Errors in Separation and Extension Proofs