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JOURNALS // Problemy Analiza — Issues of Analysis // Archive

Probl. Anal. Issues Anal., 2025 Volume 14, Issue 2, Pages 103–119 (Mi pa426)

$\mathcal{I}^\mathcal{K}$-sequential and $\mathcal{I}^\mathcal{K}$-Fréchet-Urysohn spaces

S. Roya, M. Singhab

a Sima Roy Department of Mathematics, Raja Rammohun Roy Mahavidyalaya, Hooghly, 712406, West Bengal, India
b Department of Mathematics, University of North Bengal, Darjeeling, 734013, West Bengal, India

Abstract: Notions of $\mathcal{I}^\mathcal{K}$-Fréchet-Urysohn and $\mathcal{I}^\mathcal{K}$-sequential spaces are studied by letting ideals $\mathcal{I}$, $\mathcal{K}$ of subsets of natural numbers to play measurable role in the well-established concepts of Fréchet-Urysohn and sequential spaces. Relation among those spaces in new and old setting have been established by introducing $\mathcal{I}^\mathcal{K}$-quotient maps and $\mathcal{I}^\mathcal{K}$-covering maps.

Keywords: $\mathcal{I}^\mathcal{K}$-quotient map, $\mathcal{I}^\mathcal{K}$-covering map, $\mathcal{I}^\mathcal{K}$-sequential space, $\mathcal{I}^\mathcal{K}$-Fréchet-Urysohn space.

UDC: 517.98

MSC: 40A35, 54C05, 54D55

Received: 28.11.2024
Revised: 23.04.2025
Accepted: 30.04.2025

Language: English

DOI: 10.15393/j3.art.2025.17170



© Steklov Math. Inst. of RAS, 2025