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Proceedings of the American Mathematical Society

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

 

 

The number of continua


Authors: F. W. Lozier and R. H. Marty
Journal: Proc. Amer. Math. Soc. 40 (1973), 271-273
MSC: Primary 54A25
MathSciNet review: 0328849
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Abstract: It is shown there are precisely $ {2^n}$ topologically distinct continua of weight $ n$ and power $ m$ where $ p \leqq n \leqq m$ and $ p$ is the smallest cardinal for which there is a continuum of power $ m$ and weight $ p$. In particular, there are precisely $ {2^m}$ topologically distinct continua of power $ m$.


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

  • [1] R. Engelking, Outline of general topology, Translated from the Polish by K. Sieklucki, North-Holland Publishing Co., Amsterdam; PWN-Polish Scientific Publishers, Warsaw; Interscience Publishers Division John Wiley & Sons, Inc., New York, 1968. MR 0230273
  • [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

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0328849-8
Keywords: Continuum, weight, power, long line
Article copyright: © Copyright 1973 American Mathematical Society