Spaces on which every pointwise convergent series of continuous functions converges pseudo-normally期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Lev Bukovsky Krzysztof Ciesielski

Affiliation:	Institute of Mathematics, Faculty of Sciences, P. J. Safárik University, Jesenná 5, 040~01~Kosice, Slovakia ; Department of Mathematics, West Virginia University, Morgantown, West Virginia 26506-6310

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

Keywords:	$SigmaSigma^*$-space Rothberger property quasinormal convergence pseudo-normal convergence

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