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Set Theory and Topology

Set theory provides fundamental theoretical structures for other areas of mathematics and general topology is a bridge joining set theory with applied mathematics. 

Set theory includes infinite combinatorics, convergence theory and set theoretic topology and analysis. 
Topology is the qualitative study of shapes, such as curves, surfaces, and higher dimensional manifolds. The subjects of algebraic and differential topology have connections and applications to physics, algebraic geometry, arithmetic geometry, and data sciences.