Chaos in Topological Modules
Chaotic and pathological phenomena in topological modules are studied in this manuscript. In particular, constructions of noncontinuous linear functionals are provided for a wide variety of topological modules. In addition, constructions of balanced and absorbing sets which are not neighborhoods of...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/10/526 |
| _version_ | 1827651642782121984 |
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| author | Francisco Javier García-Pacheco |
| author_facet | Francisco Javier García-Pacheco |
| author_sort | Francisco Javier García-Pacheco |
| collection | DOAJ |
| description | Chaotic and pathological phenomena in topological modules are studied in this manuscript. In particular, constructions of noncontinuous linear functionals are provided for a wide variety of topological modules. In addition, constructions of balanced and absorbing sets which are not neighborhoods of zero are also given in an extensive class of topological modules. Finally, we construct a linearly open set with empty interior in a large amount of topological modules. All these constructions are related to each other. Prior to developing all these results, we provide an axiomatization of the topological concept of limit by introducing the limit operators in a similar context as hull operators or closure operators are defined. |
| first_indexed | 2024-03-09T20:42:30Z |
| format | Article |
| id | doaj.art-1ab59c67ff9e4145bdc6d6617ba7f11e |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T20:42:30Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-1ab59c67ff9e4145bdc6d6617ba7f11e2023-11-23T22:53:48ZengMDPI AGAxioms2075-16802022-10-01111052610.3390/axioms11100526Chaos in Topological ModulesFrancisco Javier García-Pacheco0Department of Mathematics, College of Engineering, University of Cadiz, 11519 Puerto Real, SpainChaotic and pathological phenomena in topological modules are studied in this manuscript. In particular, constructions of noncontinuous linear functionals are provided for a wide variety of topological modules. In addition, constructions of balanced and absorbing sets which are not neighborhoods of zero are also given in an extensive class of topological modules. Finally, we construct a linearly open set with empty interior in a large amount of topological modules. All these constructions are related to each other. Prior to developing all these results, we provide an axiomatization of the topological concept of limit by introducing the limit operators in a similar context as hull operators or closure operators are defined.https://www.mdpi.com/2075-1680/11/10/526topological moduletopological ringbalanced setabsorbing setclosed unit neighborhood of zero |
| spellingShingle | Francisco Javier García-Pacheco Chaos in Topological Modules Axioms topological module topological ring balanced set absorbing set closed unit neighborhood of zero |
| title | Chaos in Topological Modules |
| title_full | Chaos in Topological Modules |
| title_fullStr | Chaos in Topological Modules |
| title_full_unstemmed | Chaos in Topological Modules |
| title_short | Chaos in Topological Modules |
| title_sort | chaos in topological modules |
| topic | topological module topological ring balanced set absorbing set closed unit neighborhood of zero |
| url | https://www.mdpi.com/2075-1680/11/10/526 |
| work_keys_str_mv | AT franciscojaviergarciapacheco chaosintopologicalmodules |