Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Spaces on which every pointwise convergent series of continuous functions converges pseudo-normally


Authors: Lev Bukovsky and Krzysztof Ciesielski
Journal: Proc. Amer. Math. Soc. 133 (2005), 605-611
MSC (2000): Primary 54G99, 03E35; Secondary 54A35, 54C30
Published electronically: August 25, 2004
MathSciNet review: 2093085
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A topological space $X$ is a $\Sigma\Sigma^*$-space provided that, for every sequence $\langle f_n\rangle_{n=0}^\infty$ of continuous functions from $X$ to $\mathbb{R} $, if the series $\sum_{n=0}^\infty\vert f_n\vert$ converges pointwise, then it converges pseudo-normally. We show that every regular Lindelöf $\Sigma\Sigma^*$-space has the Rothberger property. We also construct, under the continuum hypothesis, a $\Sigma\Sigma^*$-subset of $\mathbb{R} $ of cardinality continuum.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 54G99, 03E35, 54A35, 54C30

Retrieve articles in all journals with MSC (2000): 54G99, 03E35, 54A35, 54C30


Additional Information

Lev Bukovsky
Affiliation: Institute of Mathematics, Faculty of Sciences, P. J. Šafárik University, Jesenná 5, 040 01 Košice, Slovakia
Email: bukovsky@kosice.upjs.sk

Krzysztof Ciesielski
Affiliation: Department of Mathematics, West Virginia University, Morgantown, West Virginia 26506-6310
Email: K_Cies@math.wvu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07376-9
PII: S 0002-9939(04)07376-9
Keywords: $\Sigma\Sigma^*$-space, Rothberger property, quasinormal convergence, pseudo-normal convergence
Received by editor(s): January 8, 2003
Received by editor(s) in revised form: June 5, 2003
Published electronically: August 25, 2004
Additional Notes: This work was partially supported by NATO Grant PST.CLG.977652. The second author was also supported by 2002/03 West Virginia University Senate Research Grant.
Communicated by: Alan Dow
Article copyright: © Copyright 2004 American Mathematical Society