Extending families of disjoint zero sets

Author:
C. E. Aull

Journal:
Proc. Amer. Math. Soc. **89** (1983), 510-514

MSC:
Primary 54C50; Secondary 54C45, 54D60, 54G05, 54G10

DOI:
https://doi.org/10.1090/S0002-9939-1983-0715876-8

MathSciNet review:
715876

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Abstract: The -cellularity of a space is defined as

**[1]**C. E. Aull,*Extendability and expandability*(submitted for publication).**[2]**Robert L. Blair,*Spaces in which special sets are 𝑧-embedded*, Canad. J. Math.**28**(1976), no. 4, 673–690. MR**0420542**, https://doi.org/10.4153/CJM-1976-068-9**[3]**Robert L. Blair and Anthony W. Hager,*Extensions of zero-sets and of real-valued functions*, Math. Z.**136**(1974), 41–52. MR**0385793**, https://doi.org/10.1007/BF01189255**[4]**R. Engelking,*Cartesian products and dyadic spaces*, Fund. Math.**57**(1965), 287–304. MR**0196692**, https://doi.org/10.4064/fm-57-3-287-304**[5]**-,*General topology*, PWN, Warsaw, 1977.**[6]**Leonard Gillman and Meyer Jerison,*Rings of continuous functions*, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR**0116199****[7]**Takesi Isiwata,*Mappings and spaces*, Pacific J. Math. 20 (1967), 455–480; correction, ibid.**23**(1967), 630–631. MR**0219044****[8]**I. Juhász,*Cardinal functions in topology*, Mathematisch Centrum, Amsterdam, 1971. In collaboration with A. Verbeek and N. S. Kroonenberg; Mathematical Centre Tracts, No. 34. MR**0340021****[9]**R. Pol,*Short proofs of two theorems on cardinality of topological spaces*, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.**22**(1974), 1245–1249 (English, with Russian summary). MR**0383333****[10]**Michael L. Wage,*Extremally disconnected 𝑆-spaces*, Topology Proceedings, Vol. I (Conf., Auburn Univ., Auburn, Ala., 1976), Math. Dept., Auburn Univ., Auburn, Ala., 1977, pp. 181–185. MR**0458392****[11]**R. Grant Woods,*A survey of absolutes of topological spaces*, Topological structures, II (Proc. Sympos. Topology and Geom., Amsterdam, 1978) Math. Centre Tracts, vol. 116, Math. Centrum, Amsterdam, 1979, pp. 323–362. MR**565852**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0715876-8

Article copyright:
© Copyright 1983
American Mathematical Society