The existence of -sets is equivalent to the existence of strong -sets

Author:
Teodor C. Przymusiński

Journal:
Proc. Amer. Math. Soc. **79** (1980), 626-628

MSC:
Primary 54E35

DOI:
https://doi.org/10.1090/S0002-9939-1980-0572316-7

MathSciNet review:
572316

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Abstract: In this note we prove that the existence of an uncountable *Q*-set is equivalent to the existence of an uncountable strong *Q*-set, i.e. a *Q*-set all finite powers of which are *Q*-sets.

**[BBM]**R. H. Bing, W. W. Bledsoe and R. D. Mauldin,*Sets generated by rectangles*, Pacific J. Math.**51**(1974), 27-36. MR**0357124 (50:9592)****[F1]**W. G. Fleissner,*Current research on Q-sets*, Proc. Bolyai Janos Colloq. on Topology (Budapest, 1978) (to appear). MR**588793 (83j:03080)****[F2]**-,*Squares of Q-sets*(to appear).**[P]**T. C. Przymusiński,*On the equivalence of certain set theoretic and topological conditions*, Proc. Bolyai Janos Colloq. on Topology (Budapest, 1978) (to appear).**[PT]**T. C. Przymusiński and F. D. Tall,*The undecidability of the existence of a nonseparable normal Moore space satisfying the countable chain condition*, Fund. Math.**85**(1974), 291-297. MR**0367934 (51:4176)****[R]**M. E. Rudin,*Pixley-Roy and the Souslin line*, Proc. Amer. Math. Soc.**79**(1979), 128-134. MR**521886 (80c:54030)**

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DOI:
https://doi.org/10.1090/S0002-9939-1980-0572316-7

Article copyright:
© Copyright 1980
American Mathematical Society