On Certain Topological Structures of Product Normed Space Valued Paranormed Space of Summable Sequences
نویسندگان
چکیده
منابع مشابه
Menger probabilistic normed space is a category topological vector space
In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...
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On the space l of p-summable sequences (of real numbers), one can derive a norm from the 2-norm as indicated by Gunawan [6]. The purpose of this note is to establish the equivalence between such a norm and the usual norm on l. We show that our result is useful in understanding the topology of l as a 2-normed space.
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The subset the set of l1-real sequences of the linear space of real sequences is defined by the condition (Def. 1). (Def. 1) Let x be a set. Then x ∈ the set of l1-real sequences if and only if x ∈ the set of real sequences and idseq(x) is absolutely summable. Let us observe that the set of l1-real sequences is non empty. One can prove the following two propositions: (1) The set of l1-real sequ...
متن کاملmenger probabilistic normed space is a category topological vector space
in this paper, we formalize the menger probabilistic normed space as a category in which its objects are the menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. so, we can easily apply the results of topological vector spaces...
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ژورنال
عنوان ژورنال: Journal of Institute of Science and Technology
سال: 2015
ISSN: 2467-9240
DOI: 10.3126/jist.v19i1.13822