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Proceedings of the American Mathematical Society

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

 

 

Sequential order and spaces $ S\sb{n}$


Author: M. Rajagopalan
Journal: Proc. Amer. Math. Soc. 54 (1976), 433-438
DOI: https://doi.org/10.1090/S0002-9939-1976-0394576-7
MathSciNet review: 0394576
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Abstract | References | Additional Information

Abstract: It is shown that the space $ {\psi ^{\ast}}$ is a sequential space of order $ 2$ which does not contain a copy of $ {S_2}$. This solves a problem of Franklin and J. R. Boone. It is shown that there is a sequential space of order $ 4$ and not of sequential order $ 3$ but which still does not contain $ {S_3}$. It is shown that for strongly sequential, and also for countable spaces, the problem of Franklin and Boone has an affirmative answer. Some open problems are raised.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0394576-7
Keywords: Sequential order, strongly sequential, $ {S_2}$, $ {S_n}$, Fréchet space
Article copyright: © Copyright 1976 American Mathematical Society