Answer to Question #116434 in Differential Geometry | Topology for Sheela John

Question

Prove or disprove every topological space is metrizible

Answer 1

There are examples of non Hausdorff spaces (we can consider R with double zero: two points at zero, and the same topology as standard R), but every metrizible topological space is Hausdorff, so not every topological space is metrizible.