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Proceedings of the American Mathematical Society

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

 

 

Preimages of points under the natural map from $ \beta (N\times N)$ to $ \beta N\times \beta N$


Author: Neil Hindman
Journal: Proc. Amer. Math. Soc. 37 (1973), 603-608
MSC: Primary 54D35
MathSciNet review: 0358695
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Abstract: This paper deals with the size of the preimages of points of $ \beta N \times \beta N$ under the continuous extension, $ \tau $, of the identity map on $ N \times N$. It is concerned with those points $ (p,q)$ of $ \beta N \times \beta N$ for which $ {\tau ^{ - 1}}(p,q)$ is infinite and extends the work of Blass [1] who thoroughly considered those points with finite preimages.


References [Enhancements On Off] (What's this?)

  • [1] Andreas Blass, Orderings of ultrafilters, Thesis, Harvard University, Cambridge, Mass., 1970.
  • [2] 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
  • [3] Neil Hindman, On P-like spaces and their product with P-spaces, Thesis, Wesleyan University, Middletown, Conn., 1969.

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DOI: https://doi.org/10.1090/S0002-9939-1973-0358695-0
Article copyright: © Copyright 1973 American Mathematical Society