دورية أكاديمية
Ways of obtaining topological measures on locally compact spaces
| العنوان: | Ways of obtaining topological measures on locally compact spaces |
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| المؤلفون: | S. V. Butler |
| المصدر: | Известия Иркутского государственного университета: Серия "Математика", Vol 25, Iss 1, Pp 33-45 (2018) |
| بيانات النشر: | Irkutsk State University, 2018. |
| سنة النشر: | 2018 |
| المجموعة: | LCC:Mathematics |
| مصطلحات موضوعية: | topological measure, deficient topological measure, solid-set function, super-measure, q-function, Mathematics, QA1-939 |
| الوصف: | Topological measures and quasi-linear functionals generalize measures and li\-near functionals. Deficient topological measures, in turn, generalize topological measures. In this paper we continue the study of topological measures on locally compact spaces. For a compact space the existing ways of obtaining topological measures are (a) a method using super-measures, (b) composition of a q-function with a topological measure, and (c) a method using deficient topological measures and single points. These techniques are applicable when a compact space is connected, locally connected, and has a certain topological characteristic, called ``genus'', equal to 0 (intuitively, such spaces have no holes). We generalize known techniques to the situation where the space is locally compact, connected, and locally connected, and whose Alexandroff one-point compactification has genus 0. We define super-measures and q-functions on locally compact spaces. We then obtain methods for generating new topological measures by using super-measures and also by composing q-functions with deficient topological measures. We also generalize an existing method and provide a new method that utilizes a point and a deficient topological measure on a locally compact space. The methods presented allow one to obtain a large variety of finite and infinite topological measures on spaces such as $ {\mathbb R}^n$, half-spaces in ${\mathbb R}^n$, open balls in ${\mathbb R}^n$, and punctured closed balls in ${\mathbb R}^n$ with the relative topology (where $n \geq 2$). |
| نوع الوثيقة: | article |
| وصف الملف: | electronic resource |
| اللغة: | English Russian |
| تدمد: | 1997-7670 2541-8785 |
| Relation: | http://mathizv.isu.ru/assets/articles/9e8ac7e1-c96a-4458-bc59-68018dc0ec41.pdf; https://doaj.org/toc/1997-7670; https://doaj.org/toc/2541-8785 |
| DOI: | 10.26516/1997-7670.2018.25.33 |
| URL الوصول: | https://doaj.org/article/4a79cf4a34a74959807df59bc161ac37 |
| رقم الأكسشن: | edsdoj.4a79cf4a34a74959807df59bc161ac37 |
| قاعدة البيانات: | Directory of Open Access Journals |
Full Text Finder | تدمد: | 19977670 25418785 |
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| DOI: | 10.26516/1997-7670.2018.25.33 |