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

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****[F1]**W. G. Fleissner,*Current research on 𝑄 sets*, Topology, Vol. I (Proc. Fourth Colloq., Budapest, 1978) Colloq. Math. Soc. János Bolyai, vol. 23, North-Holland, Amsterdam-New York, 1980, pp. 413–431. MR**588793****[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. Przymusiński and F. D. Tall,*The undecidability of the existence of a non-separable normal Moore space satisfying the countable chain condition*, Fund. Math.**85**(1974), 291–297. MR**0367934****[R]**Mary Ellen Rudin,*Pixley-Roy and the Souslin line*, Proc. Amer. Math. Soc.**74**(1979), no. 1, 128–134. MR**521886**, 10.1090/S0002-9939-1979-0521886-5

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

Article copyright:
© Copyright 1980
American Mathematical Society