理想拓扑空间的大小归纳维数

IF 0.6 Q3 MATHEMATICS

Applied general topology Pub Date : 2021-10-01 DOI:10.4995/agt.2021.15231

F. Sereti

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引用次数: 0

摘要

毫无疑问，拓扑空间的小归纳维数ind和大归纳维数ind得到了广泛的研究，成为拓扑学的一个重要领域。它们的许多性质已经被详细研究过(例如参见[1,4,5,9,10,18])。然而，理想拓扑空间的维数研究还处于起步阶段。覆盖维度dim是这一事实的一个例外，因为它是维度的含义，[17]已经对这类空间进行了研究。本文基于小维和大维的概念，研究了理想拓扑空间的新型维。它们被称为*小和*大归纳维数，理想小和理想大归纳维数。研究了这些维数的基本性质，探讨了这些维数之间的关系。

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Small and large inductive dimension for ideal topological spaces

Undoubtedly, the small inductive dimension, ind, and the large inductive dimension, Ind, for topological spaces have been studied extensively, developing an important field in Topology. Many of their properties have been studied in details (see for example [1,4,5,9,10,18]). However, researches for dimensions in the field of ideal topological spaces are in an initial stage. The covering dimension, dim, is an exception of this fact, since it is a meaning of dimension, which has been studied for such spaces in [17]. In this paper, based on the notions of the small and large inductive dimension, new types of dimensions for ideal topological spaces are studied. They are called *-small and *-large inductive dimension, ideal small and ideal large inductive dimension. Basic properties of these dimensions are studied and relations between these dimensions are investigated.

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来源期刊

Applied general topology MATHEMATICS-

CiteScore

1.20

自引率

25.00%

发文量

审稿时长

15 weeks

期刊介绍： The international journal Applied General Topology publishes only original research papers related to the interactions between General Topology and other mathematical disciplines as well as topological results with applications to other areas of Science, and the development of topological theories of sufficiently general relevance to allow for future applications. Submissions are strictly refereed. Contributions, which should be in English, can be sent either to the appropriate member of the Editorial Board or to one of the Editors-in-Chief. All papers are reviewed in Mathematical Reviews and Zentralblatt für Mathematik.