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Separability of Real Normed Spaces and Its Basic Properties

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Nakasho K., Endou N.

Formalized Mathematics

2015

tom 23

nr 1

59-65

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].

Ograniczanie wyników

1 Formalized Mathematics

1 Endou N.

1 Nakasho K.

1 2015

Wyniki wyszukiwania

Separability of Real Normed Spaces and Its Basic Properties