Peano space
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A Peano space 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
- Wilard, Stephen (2004). General Topology. Dover Publications. ISBN 0-486-43479-6.
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