Determining the cohomological dimension of certain compacta

Author:
Leonard R. Rubin

Journal:
Proc. Amer. Math. Soc. **101** (1987), 371-376

MSC:
Primary 55M10; Secondary 54F45

DOI:
https://doi.org/10.1090/S0002-9939-1987-0902558-6

MathSciNet review:
902558

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Abstract | References | Similar Articles | Additional Information

Abstract: In previous work of this author and of John J. Walsh it was shown that many of the known examples of hereditarily infinite dimensional compacta have infinite cohomological dimension. In this paper, the class of compacta whose cohomological dimension is known to be infinite will be enlarged.

**[Bo]**Philip L. Bowers,*Detecting cohomologically stable mappings*, Proc. Amer. Math. Soc.**86**(1982), no. 4, 679–684. MR**674105**, https://doi.org/10.1090/S0002-9939-1982-0674105-3**[GS]**Dennis J. Garity and Richard M. Schori,*Infinite-dimensional dimension theory*, Proceedings of the 1985 topology conference (Tallahassee, Fla., 1985), 1985, pp. 59–74. MR**851201****[Po1]**Roman Pol,*Countable-dimensional universal sets*, Trans. Amer. Math. Soc.**297**(1986), no. 1, 255–268. MR**849478**, https://doi.org/10.1090/S0002-9947-1986-0849478-7**[Rul]**Leonard R. Rubin,*Hereditarily strongly infinite-dimensional spaces*, Michigan Math. J.**27**(1980), no. 1, 65–73. MR**555838****[Ru2]**Leonard R. Rubin,*Totally disconnected spaces and infinite cohomological dimension*, Proceedings of the 1982 Topology Conference (Annapolis, Md., 1982), 1982, pp. 157–166. MR**696628****[Ru3]**Leonard R. Rubin,*More compacta of infinite cohomological dimension*, Combinatorial methods in topology and algebraic geometry (Rochester, N.Y., 1982) Contemp. Math., vol. 44, Amer. Math. Soc., Providence, RI, 1985, pp. 221–226. MR**813117**, https://doi.org/10.1090/conm/044/813117**[Ru4]**Leonard R. Rubin,*Cell-like maps, dimension and cohomological dimension: a survey*, Geometric and algebraic topology, Banach Center Publ., vol. 18, PWN, Warsaw, 1986, pp. 371–376. MR**925877****[RSW]**Leonard R. Rubin, R. M. Schori, and John J. Walsh,*New dimension-theory techniques for constructing infinite-dimensional examples*, General Topology Appl.**10**(1979), no. 1, 93–102. MR**519716****[Wa1]**John J. Walsh,*A class of spaces with infinite cohomological dimension*, Michigan Math. J.**27**(1980), no. 2, 215–222. MR**568642****[Wa2]**John J. Walsh,*Dimension, cohomological dimension, and cell-like mappings*, Shape theory and geometric topology (Dubrovnik, 1981) Lecture Notes in Math., vol. 870, Springer, Berlin-New York, 1981, pp. 105–118. MR**643526**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1987-0902558-6

Keywords:
Cohomological dimension,
hereditarily infinite dimensional,
essential family,
cell-like mapping

Article copyright:
© Copyright 1987
American Mathematical Society