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Definition: Hereditary and Weakly Hereditary Properties

If every subspace of a topological space (X,\mathcal O) has a property of X, this property is said to be hereditary.

A property of X is said to be weakly hereditary, if every closed subset U\subseteq X, considered as a subspace of X has this property.

Propositions: 1 2


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References

Bibliography

  1. Steen, L.A.;Seebach J.A.Jr.: "Counterexamples in Topology", Dover Publications, Inc, 1970
  2. Jänich, Klaus: "Topologie", Springer, 2001, 7th Edition