Point-Set Topology

Rafael López is Professor of Mathematics at the University of Granada, Spain, and has taught a wide range of courses at undergraduate and graduate level, including geometry of curves and surfaces, differentiable manifolds, affine geometry, general topology and algebraic topology. His research interests are in differential geometry, elliptic differential equations and general relativity, with a particular focus on surfaces with prescribed curvature, capillary theory and variational problems on physics. He is the author of several textbooks on topology as well as a research monograph on surfaces with constant mean curvature.

“This book is intended as a companion book to intermediate or introductory texts on general topology, so it contains theorems … illustrated by many working examples (more than 160), worked exercises with full solutions (almost 300) and suggested exercises without solutions. … I hope that this valuable workbook, meeting all the requirements of demanding modern pedagogy will be widely used as companion to various textbooks and will contribute to raise the level of teaching the contemporary general topology for undergraduates.” (Włodzimierz Ślęzak, zbMATH 1554.54001, 2025)

• - Introduction.- Topological spaces.- Proximity on a topological space.- Metric spaces.- Continuity.- Homeomorphisms and topological invariants.- Product topology.- Connectedness.- Compactness.- Quotient topology.- The fundamental group.