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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


How separable is a space? That depends on your set theory!
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by Franklin D. Tall PDF
Proc. Amer. Math. Soc. 46 (1974), 310-314 Request permission


A. Wilansky has raised the question of the productive behaviour of the property of having a countable set, such that each point is a sequential limit point of the set. The set-theoretic consistency and independence of the proposition that this property is preserved by products of ${\aleph _1}$ factors is established.
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  • D. D. Booth, Countably indexed ultrafilters, Thesis, University of Wisconsin, Madison, Wis., 1969.
  • L. Bukovský, Borel subsets of metric separable spaces, General Topology and its Relations to Modern Analysis and Algebra, II (Proc. Second Prague Topological Sympos., 1966) Academia, Prague, 1967, pp. 83–86. MR 0231723
  • W. W. Comfort, A short proof of Marczewski’s separability theorem, Amer. Math. Monthly 76 (1969), 1041–1042. MR 248742, DOI 10.2307/2317135
  • N. E. Foland and R. B. Kirk, Products of spaces with $m$-dense subsets (preprint). K. Gödel, Consistency-proof for the generalized continuum hypothesis, Proc. Nat. Acad. Sci. U.S.A. 25 (1939), 220-224.
  • R. W. Heath, Screenability, pointwise paracompactness, and metrization of Moore spaces, Canadian J. Math. 16 (1964), 763–770. MR 166760, DOI 10.4153/CJM-1964-073-3
  • I. Juhász, Cardinal functions in topology, Mathematical Centre, Amsterdam, 1971.
  • D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), no. 2, 143–178. MR 270904, DOI 10.1016/0003-4843(70)90009-4
  • Fritz Rothberger, On some problems of Hausdorff and of Sierpiński, Fund. Math. 35 (1948), 29–46. MR 29958, DOI 10.4064/fm-35-1-29-46
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  • F. D. Tall, An alternative to the continuum hypothesis and its uses in general topology (preprint).
  • Albert Wilansky, Research Problems: How Separable is a Space?, Amer. Math. Monthly 79 (1972), no. 7, 764–765. MR 1536789, DOI 10.2307/2316270
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 46 (1974), 310-314
  • MSC: Primary 54B10; Secondary 54E30
  • DOI:
  • MathSciNet review: 0362188