Point-Set Topology
Topology studies properties of spaces preserved under continuous transformations, essential in understanding network topology and data analysis.
X ~ Y (homeomorphic spaces)
Algebraic Topology
Topology provides tools for analyzing topological invariants, crucial in understanding shape and structure of spaces.
π1(X) = fundamental group of X
Geometric Topology
Topology has far-reaching implications in geometry, analysis, and physics, including study of manifolds and topological invariants.
M = manifold (topological space)