On I-quotient mappings and I-cs'-networks under a maximal ideal

Authors

  • Xiangeng Zhou Ningde Normal University

DOI:

https://doi.org/10.4995/agt.2020.12967

Keywords:

ideal convergence, maximal ideal, I-sequential neighborhood, I-quotient mappings, I-cs'-networks, I-FU spaces

Abstract

Let I be an ideal on N and f : X → Y be a mapping. f is said to be an I-quotient mapping provided f−1(U) is I-open in X, then U is I-open in Y . P is called an I-cs"²-network of X if whenever {xn}n∈N is a sequence I-converging to a point x ∈ U with U open in X, then there is P ∈ P and some n0 ∈ N such that {x, xn0} ⊆ P ⊆ U. In this paper, we introduce the concepts of I-quotient mappings and I-cs"²-networks, and study some characterizations of I-quotient mappings and I-cs"²- networks, especially J -quotient mappings and J -cs"²-networks under a maximal ideal J of N. With those concepts, we obtain that if X is an J -FU space with a point-countable J -cs"²-network, then X is a meta-Lindelöf space.

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Author Biography

Xiangeng Zhou, Ningde Normal University

Department of Mathematics

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Published

2020-10-01

How to Cite

[1]
X. Zhou, “On I-quotient mappings and I-cs’-networks under a maximal ideal”, Appl. Gen. Topol., vol. 21, no. 2, pp. 235–246, Oct. 2020.

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