Peano space

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.