Separability of Real Normed Spaces and Its Basic Properties

• Autorzy: Kazuhisa Nakasho , Noboru Endou
• Języki publikacji: EN

Abstrakty

EN

In this article, the separability of real normed spaces and its properties are mainly formalized. In the first section, it is proved that a real normed subspace is separable if it is generated by a countable subset. We used here the fact that the rational numbers form a dense subset of the real numbers. In the second section, the basic properties of the separable normed spaces are discussed. It is applied to isomorphic spaces via bounded linear operators and double dual spaces. In the last section, it is proved that the completeness and reflexivity are transferred to sublinear normed spaces. The formalization is based on [34], and also referred to [7], [14] and [16].

Słowa kluczowe

EN

functional analysis; normed linear space; topological vector space

Kategorie tematyczne

• 46A19: Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than 𝐑 , etc.)
• 03B35: Mechanization of proofs and logical operations
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2015
• Tom: 23
• Numer: 1
• Strony: 59-65

Daty

wydano

2015-03-01

otrzymano

2015-02-26

online

2015-03-31

Twórcy

autor

Kazuhisa Nakasho

• Shinshu University, Nagano, Japan

autor

Noboru Endou

• Gifu National College of Technology, Gifu, Japan

Bibliografia

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Identyfikatory

DOI

10.2478/forma-2015-0005

bwmeta1.id-class.MML

NORMSP _4