What is meant by synthetic topology?

Answer 1

Synthetic topology refers to a branch of mathematics that studies topological spaces and their properties through abstract, algebraic, or categorical methods rather than traditional point-set techniques. It often involves defining topologies using structures such as frames, locales, or categories, allowing for a more conceptual understanding of topological concepts. This approach can provide insights into the nature of continuity, convergence, and other fundamental notions in topology without relying heavily on set-theoretic foundations.