A topological translation of a fundamental problem in cluster set theory
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- by J. A. Eidswick PDF
- Proc. Amer. Math. Soc. 53 (1975), 75-79 Request permission
Abstract:
Two conjectures related to the problem of finding a “large” family of approach curves along which cluster sets can be preassigned are shown to be equivalent to special cases of the normal Moore space conjecture.References
- R. H. Bing, Metrization of topological spaces, Canad. J. Math. 3 (1951), 175–186. MR 43449, DOI 10.4153/cjm-1951-022-3
- R. H. Bing, A translation of the normal Moore space conjecture, Proc. Amer. Math. Soc. 16 (1965), 612–619. MR 181976, DOI 10.1090/S0002-9939-1965-0181976-6
- E. F. Collingwood and A. J. Lohwater, The theory of cluster sets, Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge University Press, Cambridge, 1966. MR 0231999
- J. A. Eidswick, On some fundamental problems in cluster set theory, Proc. Amer. Math. Soc. 39 (1973), 163–168. MR 313454, DOI 10.1090/S0002-9939-1973-0313454-X William Fleissner, Thesis, University of California, Berkeley, Calif., 1974.
- William Fleissner, Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), 294–298. MR 362240, DOI 10.1090/S0002-9939-1974-0362240-4 —, When is Jones’ space normal? Proc. Amer. Math. Soc. (submitted). E. W. Hobson, The theory of functions of a real variable. Vol. 1, 3rd ed., Dover, New York, 1957.
- Kiyoshi Noshiro, Cluster sets, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 28, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960. MR 0133464 Neil G. Smith, On a set-theoretic offshoot of the normal Moore space question, Thesis, University of Nebraska, 1973.
- L. A. Steen, Conjectures and counterexamples in metrization theory, Amer. Math. Monthly 79 (1972), 113–132. MR 309075, DOI 10.2307/2316532 F. D. Tall, Set-theoretic consistency results and topological theorems concerning the normal Moore space conjecture and related problems, Thesis, University of Wisconsin, Madison, Wis., 1969.
- Franklin D. Tall, New results on the normal Moore space problem, Proc. Washington State Univ. Conf. on General Topology (Pullman, Wash., 1970) Washington State University, Department of Mathematics, Pi Mu Epsilon, Pullman, Wash., 1970, pp. 120–126. MR 0264603
- Franklin D. Tall, A set-theoretic proposition implying the metrizability of normal Moore spaces, Proc. Amer. Math. Soc. 33 (1972), 195–198. MR 300239, DOI 10.1090/S0002-9939-1972-0300239-2
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 75-79
- MSC: Primary 26A54; Secondary 30A72, 54E30
- DOI: https://doi.org/10.1090/S0002-9939-1975-0376983-0
- MathSciNet review: 0376983