Affiliation:
1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, P.R. China
Abstract
In this paper, we define several ideal versions of Cauchy sequences and
completeness in quasimetric spaces. Some examples are constructed to clarify
their relationships. We also show that: (1) if a quasi-metric space (X, ?)
is I-sequentially complete, for each decreasing sequence {Fn} of nonempty
I-closed sets with diam{Fn} ? 0 as n ? ?, then ?n?N Fn is a single-point
set; (2) let I be a P-ideal, then every precompact left I-sequentially
complete quasi-metric space is compact.
Publisher
National Library of Serbia
Reference37 articles.
1. M. Balcerzak, M. Poplawski, A. Wachowicz, The Baire category of ideal convergent subseries and rearrangements, Topology. Appl. 231 (2017) 219-230.
2. L. Bao, L. Cheng, On statistical measure theory, J. Math. Anal. Appl. 407 (2013) 413-424.
3. H. Cakalli, On statistical convergence in topological groups, Pure. Appl. Math. Sci. Slovaca. 43 (1996) 27-31.
4. H. Cakalli, A study on statistical convergence, Funct. Anal. Apprrox. Comput. 1 (2) (2009) 19-24.
5. A. Caserta, Lj.D.R. Kočinac, On statistical exhaustiveness, Appl. Math. Letters 25 (2012) 1447-1451.
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