Page "Surface" Paragraph 4

A ( topological ) surface is a nonempty second countable Hausdorff topological space in which every point has an open neighbourhood homeomorphic to some open subset of the Euclidean plane E < sup > 2 </ sup >.

Such a neighborhood, together with the corresponding homeomorphism, is known as a ( coordinate ) chart.

It is through this chart that the neighborhood inherits the standard coordinates on the Euclidean plane.

These coordinates are known as local coordinates and these homeomorphisms lead us to describe surfaces as being locally Euclidean.