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Transactions of the American Mathematical Society

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

 
 

 

Concerning first countable spaces. III


Author: G. M. Reed
Journal: Trans. Amer. Math. Soc. 210 (1975), 169-177
MSC: Primary 54E30
DOI: https://doi.org/10.1090/S0002-9947-1975-0372828-8
MathSciNet review: 0372828
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Abstract: The primary purpose of this paper is (1) to provide a ``real'' example of a regular first countable $ {T_1}$-space which has no dense developable subspace and (2) to provide a new technique for producing Moore spaces which fail to have dense metrizable subspaces. Related results are established which produce new examples of noncompletable Moore spaces and which show that each regular hereditary $ M$-space with a $ {G_\delta }$-diagonal has a dense metrizable subspace.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0372828-8
Article copyright: © Copyright 1975 American Mathematical Society

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