CLOPEN LINEAR SUBSPACES AND CONNECTEDNESS IN FUNCTION SPACES

被引：1

作者：

Chauhan, Tarun kumar ^{[1
]}

Jindal, Varun ^{[2
]}

机构：

[1] BK Birla Inst Higher Educ, Dept Math, Pilani, India

[2] Malaviya Natl Inst Technol, Dept Math, Jaipur, India

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2023年 / 53卷 / 05期

关键词：

bornology; clopen linear subspaces; connectedness; real continuous functions; shield; strong uniform convergence; strong Whitney convergence; M-TOPOLOGY; BORNOLOGIES; CONVERGENCE;

D O I：

10.1216/rmj.2023.53.1415

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We aim to study clopen linear subspaces and connectedness properties of the space C(X) of all real-valued continuous functions defined on a metric space (X, d) equipped with various topologies. In particular, we consider the topologies of strong Whitney and strong uniform convergence on bornology. We also examine when these topologies on C(X) are locally convex. While studying clopen subspaces, we give new characterizations for the notion of a shield and for a bornology to be shielded from closed sets.

引用

页码：1415 / 1430

页数：16

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