A Study on Strongly Lacunary Ward Continuity in 2-Normed Spaces

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-15 DOI:10.1134/s0001434624050262

Sibel Ersan

引用次数: 0

Abstract

In this paper, we study the ideal strong lacunary ward compactness of a subset of a 2-normed space \(X\) and the ideal strongly lacunary ward continuity of a function \(f\) on \(X\). Here a subset \(E\) of \(X\) is said to be ideal strong lacunary ward compact if any sequence in \(E\) has an ideal strong lacunary quasi-Cauchy subsequence. Additionally, a function on \(X\) is said to be ideal strong lacunary ward continuous if it preserves ideal strong lacunary quasi-Cauchy sequences; an ideal is defined to be a hereditary and additive family of subsets of \(\mathbb{N}\). We find that a subset \(E\) of \(X\) with a countable Hamel basis is totally bounded if and only if it is ideal strong lacunary ward compact.

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关于 2 规范空间中强空白区连续性的研究

摘要本文研究了2规范空间\(X\) 子集的理想强割裂紧凑性以及函数\(f\) 在\(X\) 上的理想强割裂连续性。这里，如果 \(E\) 中的任何序列都有一个理想的强疏松准考奇子序列，那么就可以说 \(X\) 的子集 \(E\) 是理想的强疏松紧凑的。此外，如果在 \(X\) 上的一个函数保留了理想的强缺陷准考奇序列，那么这个函数就被称为理想的强缺陷连续函数；理想的定义是 \(\mathbb{N}\) 子集的一个遗传的、可加的族。我们发现，具有可数哈梅尔基的\(X)的子集\(E\)是完全有界的（当且仅当它是理想的强拉克希准紧凑时）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.