Extending families of disjoint zero sets
Author:
C. E. Aull
Journal:
Proc. Amer. Math. Soc. 89 (1983), 510514
MSC:
Primary 54C50; Secondary 54C45, 54D60, 54G05, 54G10
MathSciNet review:
715876
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Abstract: The cellularity of a space is defined as where is the family of zero sets of . It is proved using CH that a Tychonoff space is embedded in every Tychonoff space it is embedded in iff . A space is defined to be embedded in a space if any disjoint family of zero sets of can be extended to a family of disjoint zero sets of . Similar theorems are proved for embedding when is a space or the zero sets have the Isiwata property.
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 [1]
 C. E. Aull, Extendability and expandability (submitted for publication).
 [2]
 R. L. Blair, Spaces in which special sets are embedded, Canad. J. Math. 28 (1976), 673690. MR 0420542 (54:8556)
 [3]
 R. L. Blair and A. W. Hager, Extensions of zerosets and of realvalued functions, Math. Z. 136 (1974), 4152. MR 0385793 (52:6652)
 [4]
 R. Engelking, Cartesian products and dyadic spaces, Fund. Math. 57 (1965), 287306. MR 0196692 (33:4879)
 [5]
 , General topology, PWN, Warsaw, 1977.
 [6]
 L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, Princeton, N. J., 1966. MR 0116199 (22:6994)
 [7]
 T. Isiwata, Mappings and spaces, Pacific J. Math. 20 (1967), 455480. MR 0219044 (36:2127)
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 I. Juhasz, Cardinal functions in topology, Math. Centre Tracts, No. 34, Mathematisch Centrum, Amsterdam, 1971. MR 0340021 (49:4778)
 [9]
 R. Pol, Short proofs of two theorems of cardinality of topological spaces, Bull. Acad. Polon. Sci. Sér. Math. 22 (1974), 12451249. MR 0383333 (52:4214)
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 M. Wage, Extremally disconnected spaces, Topology Proc. (Conf. Auburn Univ. Auburn, Ala, 1976), Math. Dept., Auburn Univ., Auburn, 1977, pp. 181186. MR 0458392 (56:16595)
 [11]
 R. G. Woods, Absolutes of topological spaces, Math. Centre Tracts, No. 116, Mathematisch Centrum, Amsterdam, 1979, pp. 323362. MR 565852 (81d:54019)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198307158768
PII:
S 00029939(1983)07158768
Article copyright:
© Copyright 1983
American Mathematical Society
