Tag: continuous maps

• Continuous Maps and Homeomorphisms: Continuity Recast through Preimages of Open SetsContinuity is defined by requiring preimages of open sets to be open; we prove this agrees with ε-δ continuity on metric spaces, and compute in full why R is homeomorphic to (0,1) but not to [0,1].MathematicsGeneral TopologyGraduatetopological spacescontinuous mapshomeomorphismtopological invariants~26 min