Sequential order and spaces 𝑆_{𝑛}

Rajagopalan, M.

doi:10.1090/S0002-9939-1976-0394576-7

Sequential order and spaces $S_{n}$
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Proc. Amer. Math. Soc. 54 (1976), 433-438 Request permission

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

Journal: Proc. Amer. Math. Soc. 54 (1976), 433-438
DOI: https://doi.org/10.1090/S0002-9939-1976-0394576-7
MathSciNet review: 0394576