Peano space

Peano space

In point-set topology, a branch of mathematics, a Peano space, named after Giuseppe Peano, is a compact, connected, locally connected metric space.

Properties

*Every Peano space is arcwise connected, more generally every open connected subset of a Peano space is arcwise connected.
*Hahn-Mazurkiewicz theorem: A Hausdorff space is a continuous image of the unit interval if and only if it is a Peano space.

References

*cite book | author=Wilard, Stephen | title=General Topology | publisher=Dover Publications | year=2004 | id=ISBN 0-486-43479-6


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