Geodesic
On I-covering images of metric spaces
Filomat, Tome 36 (2022) no. 19, p. 6621

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DOI

Let I be an ideal on N. A mapping f : X → Y is called an I-covering mapping provided a sequence {yn}n∈N is I-converging to a point y in Y, there is a sequence {xn}n∈N converging to a point x in X such that x ∈ f −1(y) and each xn ∈ f −1(yn). In this paper we study the spaces with certain I-cs-networks and investigate the characterization of the images of metric spaces under certain I-covering mappings, which prompts us to discover I-cs f -networks. The following main results are obtained: (1) A space X has an I-cs f -network if and only if X is a continuous and I-covering image of a metric space. (2) A space X is an I-cs f -countable space if and only if X is a continuous I-covering and boundary s-image of a metric space. (3) A space X has a point-countable I-cs-network if and only if X is a continuous I-covering and s-image of a metric space.
DOI : 10.2298/FIL2219621Z
Classification : 54A20, 54B15, 54C08, 54C10, 54D55 54E20, 54E40, 54E99
Keywords: Ideal, I-convergence, I-cs-network, I-covering mapping, I-sequential space, I-FU-space 
Xiangeng Zhou; Shou Lin. On I-covering images of metric spaces. Filomat, Tome 36 (2022) no. 19, p. 6621 . doi: 10.2298/FIL2219621Z
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     author = {Xiangeng Zhou and Shou Lin},
     title = {On {I-covering} images of metric spaces},
     journal = {Filomat},
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     year = {2022},
     volume = {36},
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     doi = {10.2298/FIL2219621Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2219621Z/}
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