Peano space

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

Definition

Symbol-free definition

A Peano space is a space which satisfies the following equivalent conditions:

• There is a continuous surjective map from the closed unit interval $[0,1]$ to the given space, and the space is Hausdorff
• The space is Hausdorff, compact, connected, metrizable, and locally connected

Equivalence of definitions

The two definitions are equivalent via the Hahn-Mazurkiewicz theorem.