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## Colloquium Mathematicum

1999 | 80 | 2 | 297-307
Tytuł artykułu

### Tightness and π-character in centered spaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We continue an investigation into centered spaces, a generalization of dyadic spaces. The presence of large Cantor cubes in centered spaces is deduced from tightness considerations. It follows that for centered spaces X, πχ(X) = t(X), and if X has uncountable tightness, then t(X) = sup{κ : $2^κ$ ⊂ X}. The relationships between 9 popular cardinal functions for the class of centered spaces are justified. An example is constructed which shows, unlike the dyadic and polyadic properties, that the centered property is not preserved by passage to a zeroset.
Słowa kluczowe
EN
Czasopismo
Rocznik
Tom
Numer
Strony
297-307
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-09-28
poprawiono
1999-03-01
Twórcy
autor
• Department of Mathematics University of Manitoba Winnipeg, Manitoba Canada R3T 2N2
Bibliografia
• [1] A. Arkhangel'skiĭ, Approximation of the theory of dyadic bicompacta, Soviet Math. Dokl. 10 (1969), 151-154.
• [2] A. Arkhangel'skiĭ, On bicompacta hereditarily satisfying Suslin's condition. Tightness and free sequences, ibid. 12 (1971), 1253-1257.
• [3] A. Arkhangel'skiĭ, Structure and classification of topological spaces and cardinal invariants, Russian Math. Surveys 33 (1978), no. 6, 33-96.
• [4] M. Bell, Generalized dyadic spaces, Fund. Math. 125 (1985), 47-58.
• [5] M. Bell, $G_κ$ subspaces of hyadic spaces, Proc. Amer. Math. Soc. 104 (1988), 635-640.
• [6] J. Gerlits, On subspaces of dyadic compacta, Studia Sci. Math. Hungar. 11 (1976), 115-120.
• [7] J. Gerlits, On a generalization of dyadicity, ibid. 13 (1978), 1-17.
• [8] I. Juhász, Cardinal Functions in Topology--Ten Years Later, Math. Centre Tracts 123, Mathematisch Centrum, Amsterdam, 1980.
• [9] I. Juhász and S. Shelah, $π(X) = δ(X)$ for compact $X$, Topology Appl. 32 (1989), 289-294.
• [10] W. Kulpa and M. Turzański, Bijections onto compact spaces, Acta Univ. Carolin. Math. Phys. 29 (1988), 43-49.
• [11] G. Plebanek, Compact spaces that result from adequate families of sets, Topology Appl. 65 (1995), 257-270.
• [12] G. Plebanek, Erratum to 'Compact spaces that result from adequate families of sets', ibid. 72 (1996), 99.
• [13] B. Shapirovskiĭ, Maps onto Tikhonov cubes, Russian Math. Surveys 35 (1980), no. 3, 145-156.
• [14] M. Talagrand, Espaces de Banach faiblement K-analytiques, Ann. of Math. 110 (1979), 407-438.
• [15] S. Todorčević, Remarks on cellularity in products, Compositio Math. 57 (1986), 357-372.
• [16] M. Turzański, On generalizations of dyadic spaces, Acta Univ. Carolin. Math. Phys. 30 (1989), 153-159.
• [17] M. Turzański, Cantor cubes: chain conditions, Prace Nauk. Uniw. Śląsk. Katowic. 1612 (1996).
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Bibliografia
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