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Article

Turzański, Marian
Strong sequences and the weight of regular spaces. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 33 (1992), issue 3, pp. 557-561
MSC: 05A99, 54A25, 54D10 | MR 1209297 | Zbl 0793.54016
Keywords:
strong sequence; Cantor discontinuum; dyadic space; cellularity and weight of space
Summary:
It will be shown that if in a family of sets there exists a strong sequence of the length $(\kappa ^{\lambda })^+$ then this family contains a subfamily consisting of $\lambda ^+$ pairwise disjoint sets. The method of strong sequences will be used for estimating the weight of regular spaces.
References:
[1] Efimov B.A.: Diaditcheskie bikompakty (in Russian). Trudy Mosk. Matem. O-va 14 (1965), 211-247. MR 0202105
[2] Efimov B.A.: Ob ekstremal'no nesvjaznych bikompaktach $\pi $-vesa kontinuum (in Russian). DAN 183 , no. 3 (1968), 15-18. MR 0236878
[3] Efimov B.A.: Ekstremal'no nesvjaznye bikompakty (in Russian). Trudy Mosk. Matem. O-va 23 (1970), 235-276. MR 0418016
[4] Hodel R.: Cardinal Functions I. Handbook of Set-Theoretic Topology, North-Holland, 1984. MR 0776620 | Zbl 0559.54003
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