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 to the given space, and the space is Hausdorff
- The space is Hausdorff, compact, connected, metrizable, and locally connected
![{\displaystyle [0,1]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/738f7d23bb2d9642bab520020873cccbef49768d)
Equivalence of definitions
The two definitions are equivalent via the Hahn-Mazurkiewicz theorem.