Geodesic
A note on I-convergence in quasi-metric spaces
Filomat, Tome 37 (2023) no. 4, p. 1133

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DOI

In this paper, we define several ideal versions of Cauchy sequences and completeness in quasi-metric spaces. Some examples are constructed to clarify their relationships. We also show that: (1) if a quasi-metric space (X, ρ) is I-sequentially complete, for each decreasing sequence {F n } of nonempty I-closed sets with diam{F n } → 0 as n → ∞, then n∈N F n is a single-point set; (2) let I be a P-ideal, then every precompact left I-sequentially complete quasi-metric space is compact.
DOI : 10.2298/FIL2304133T
Classification : 54A20, 40A05, 40A99, 54E35
Keywords: Quasi-metric space, P-ideal, I-Cauchy sequence, I-completeness 
Zhongbao Tang; Qian Xiong. A note on I-convergence in quasi-metric spaces. Filomat, Tome 37 (2023) no. 4, p. 1133 . doi: 10.2298/FIL2304133T
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     title = {A note on {I-convergence} in quasi-metric spaces},
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     doi = {10.2298/FIL2304133T},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2304133T/}
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