函数空间中的闭线性子空间与连通性

IF 0.7 4区数学 Q2 MATHEMATICS Rocky Mountain Journal of Mathematics Pub Date : 2023-10-01 DOI:10.1216/rmj.2023.53.1415

Tarun Kumar Chauhan, Varun Jindal

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引用次数: 0

摘要

研究定义在具有各种拓扑的度量空间(X,d)上的所有实值连续函数的闭线性子空间及其空间C(X)的连通性。特别地，我们考虑了bornology上的强惠特尼和强一致收敛拓扑。我们还研究了C(X)上的这些拓扑何时是局部凸的。在研究闭子空间的过程中，我们给出了屏蔽的概念和对闭集屏蔽的本体的新的表征。

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CLOPEN LINEAR SUBSPACES AND CONNECTEDNESS IN FUNCTION SPACES

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.

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来源期刊

Rocky Mountain Journal of Mathematics 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

审稿时长

7.5 months

期刊介绍： Rocky Mountain Journal of Mathematics publishes both research and expository articles in mathematics, and particularly invites well-written survey articles. The Rocky Mountain Journal of Mathematics endeavors to publish significant research papers and substantial expository/survey papers in a broad range of theoretical and applied areas of mathematics. For this reason the editorial board is broadly based and submissions are accepted in most areas of mathematics. In addition, the journal publishes specialized conference proceedings.

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