Topology (Point-Set)

The study of spaces and continuity without distance: open sets, compactness, connectedness, separation axioms, and quotient spaces. The abstract foundation for modern geometry and analysis.

Course Overview

Textbook

Munkres, Topology

Chapters

TBD

Sections

TBD

Prerequisites

Real Analysis I

Target

Foundation for Algebraic Topology, Differential Geometry, Functional Analysis

Status

Planned

Chapters will be scaffolded when this course becomes active.

Why This Course

  • Analysis — every advanced analysis result uses topological arguments

  • Data science — topological data analysis (TDA) extracts shape from data

  • Computer science — domain theory in programming language semantics

  • Physics — topological phases of matter, gauge theory

  • Foundation — unlocks Algebraic Topology, Manifold Theory, Functional Analysis