Non-existence of certain topological expansions

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This note proves the following theorem:

Theorem. — For For every cardinal τ that τ>2c there exists a completely regular space of dispersion character τ which cannot be expanded to a normal space without changing the dispersion character.

This result answers a question raised by Edwin Hewitt.


  1. [1]

    Edwin Hewitt,A problem of set-theoretic topology, Duke Mathematical Jonrnal, vol. 10 (1943), pp. 309–333.

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Dedicated to the sixtieth birthday of Frof. Edgar R. Lorch

This research was supported in part by the National Science Foundation, U.S.A.

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Tong, H. Non-existence of certain topological expansions. Annali di Matematica 86, 43–45 (1970).

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  • Normal Space
  • Regular Space
  • Dispersion Character
  • Topological Expansion