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Sahand Communications in Mathematical Analysis، جلد ۲۱، شماره ۴، صفحات ۲۷-۴۲
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عنوان انگلیسی A Version of the Hahn-Banach Theorem for R-Vector Spaces
چکیده انگلیسی مقاله Recently, $R$-metric spaces have been introduced to generalized metric spaces. This extension is based on the construction of a new universe with interesting properties. In this paper, some topological properties of $R$-metric spaces are studied and compared to the classical metric spaces via several examples. Also, some properties of a metric space with different relations are considered. Then, the elementary tools needed for the study of two important theorems of functional analysis are presented. For example, $R$-sequentially bounded sets, $R$-bounded sets, $R$-sequentially bounded functions and $R$-bounded functions are introduced in $R$-metric spaces. Moreover, a condition is given under which an $R$-continuous function is $R$-sequentially bounded. Finally, variants of the Heine--Borel theorem and the Hahn--Banach theorem are proved for $R$-metric spaces and $R$-vector spaces, respectively.
کلیدواژه‌های انگلیسی مقاله Hahn Banach theorem,R-connected set,R-compact set,R-continuous function,R-metric space
نویسندگان مقاله Azadeh Alijani |
Vali-e-Asr University of Rafsanjan, Department of Mathematics, Rafsanjan, Iran. ORDID: 0000-0001-7851-8684.

Zohreh Heydarpour |
Department of mathematics, Payame Noor University (PNU), P. O. Box 19395-4697, Tehran, Iran.

Maryam Naderi Parizi |
Department of mathematics, Payame Noor University (PNU), P. O. Box 19395-4697, Tehran, Iran.

نشانی اینترنتی https://scma.maragheh.ac.ir/article_713438_dcfae09d3cc9154ad27593c9326e34fa.pdf
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