I: Fréchet-Urysohn spaces

Renukadevi, V.; Prakash, Bharath Ravi

doi:10.5937/matmor1602087r

Cited by 7 publications

(2 citation statements)

References 14 publications

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“…Later B.K. Lahiri and P. Das in [12] discussed convergence in I and in I * and investigate some additional results related to mentioned concepts [4,[8][9][10][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

$\mathcal{I}^{\mathcal{K}}$-SEQUENTIAL TOPOLOGY

Behmanush,

Küçükaslan

2023

UMJ

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In the literature, $\mathcal{I}$-convergence (or convergence in $\mathcal{I}$) was first introduced in [11]. Later related notions of $\mathcal{I}$-sequential topological space and $\mathcal{I}^*$-sequential topological space were introduced and studied. From the definitions it is clear that $\mathcal{I}^*$-sequential topological space is larger(finer) than $\mathcal{I}$-sequential topological space. This rises a question: is there any topology (different from discrete topology) on the topological space $\mathcal{X}$ which is finer than $\mathcal{I}^*$-topological space? In this paper, we tried to find the answer to the question. We define $\mathcal{I}^{\mathcal{K}}$-sequential topology for any ideals $\mathcal{I}$, $\mathcal{K}$ and study main properties of it. First of all, some fundamental results about $\mathcal{I}^{\mathcal{K}}$-convergence of a sequence in a topological space $(\mathcal{X} ,\mathcal{T})$ are derived. After that, $\mathcal{I}^{\mathcal{K}}$-continuity and the subspace of the $\mathcal{I}^{\mathcal{K}}$-sequential topological space are investigated.

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“…Later B.K. Lahiri and P. Das in [12] discussed convergence in I and in I * and investigate some additional results related to mentioned concepts [4,[8][9][10][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

$\mathcal{I}^{\mathcal{K}}$-SEQUENTIAL TOPOLOGY

Behmanush,

Küçükaslan

2023

UMJ

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“…Lemma 1.1. [10] Let f : X → Y be a quotient mapping and X be an I-Fréchet-Urysohn space. Then Y is an I-Fréchet-Urysohn space if and only if f is pseudo open.…”

Section: Introductionmentioning

confidence: 99%