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.
Edwin Hewitt,A problem of set-theoretic topology, Duke Mathematical Jonrnal, vol. 10 (1943), pp. 309–333.
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). https://doi.org/10.1007/BF02415707
- Normal Space
- Regular Space
- Dispersion Character
- Topological Expansion