Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

 

 

Spaces of countable and point-countable type


Author: J. E. Vaughan
Journal: Trans. Amer. Math. Soc. 151 (1970), 341-351
MSC: Primary 54.40
DOI: https://doi.org/10.1090/S0002-9947-1970-0266157-6
MathSciNet review: 0266157
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: These spaces were introduced by M. Henriksen and J. R. Isbell, and A. V. Arhangel'skiĭ, who proved results about the placement of such spaces in their compactifications. In the present paper, these results are consolidated using new terminology. In addition, further results concerning the heredity of these spaces are obtained. Generalizations of these spaces are introduced, and an analogous treatment is given for them. Finally, some examples are given of which one gives a solution to a problem raised by Arhangel'skiĭ by showing that the perfect image of a first countable space need not be of point-countable type.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54.40

Retrieve articles in all journals with MSC: 54.40


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1970-0266157-6
Keywords: Spaces of countable type, spaces of point-countable type, Tychonoff spaces, character of a set, pseudocharacter of a set, compactifications, Stone-Čech compactifications, generalized $ {F_\sigma }$, Q-closed, real-compact
Article copyright: © Copyright 1970 American Mathematical Society