Elastic 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

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Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Metrizable space	underlying topology of a metric space	metrizable implies elastic	elastic not implies metrizable	Protometrizable space|FULL LIST, MORE INFO
Manifold		(via metrizable)		Metrizable space, Protometrizable space|FULL LIST, MORE INFO
Sub-Euclidean space
Closed sub-Euclidean space				Metrizable space, Protometrizable space|FULL LIST, MORE INFO

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
paracompact Hausdorff space	paracompact and Hausdorff	elastic implies paracompact Hausdorff	paracompact Hausdorff not implies elastic	|FULL LIST, MORE INFO
monotonically normal space				|FULL LIST, MORE INFO
hereditarily collectionwise normal space				Monotonically normal space|FULL LIST, MORE INFO
hereditarily normal space	every subspace is normal			Hereditarily collectionwise normal space, Monotonically normal space|FULL LIST, MORE INFO
collectionwise normal space	$T_{1}$, and any discrete collection of closed subsets can be separated by disjoint open subsets			Hereditarily collectionwise normal space, Monotonically normal space|FULL LIST, MORE INFO
normal space	$T_{1}$, and any two disjoint closed subsets are separated by disjoint open subsets			Collectionwise normal space, Hereditarily collectionwise normal space, Hereditarily normal space, Monotonically normal space|FULL LIST, MORE INFO

References

• Paracompactness and elastic spaces by Hisahiro Tamano and J. E. Vaughan, Proc. Am. Math. Soc., Vol. 28. No. 1 (Apr 1971) pp. 299-303