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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Minimal convergence spaces


Authors: D. C. Kent and G. D. Richardson
Journal: Trans. Amer. Math. Soc. 160 (1971), 487-499
MSC: Primary 54.22
DOI: https://doi.org/10.1090/S0002-9947-1971-0286063-1
MathSciNet review: 0286063
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Abstract: We are primarily concerned with minimal $ {\text{P}}$ convergence spaces, where $ {\text{P}}$ is one of the following convergence space properties: Hausdorff, $ {{\text{T}}_2}, \lambda $-regular, $ \lambda $-Urysohn, and first countable, $ \lambda $ an infinite cardinal number. Our conclusions usually resemble the corresponding topological results, but with some deviations ; for instance, a minimal Hausdorff convergence space is always compact, whereas a countable minimal regular convergence space need not be compact.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0286063-1
Keywords: Convergence spaces, minimal $ {\text{P}}$ convergence spaces, $ {\text{P}}$-closed convergence spaces, $ \lambda $-regular convergence spaces, $ \lambda $-Urysohn convergence spaces
Article copyright: © Copyright 1971 American Mathematical Society

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