Displaying similar documents to “Generalized degree in normed spaces.”

Orthogonality in normed linear spaces: a classification of the different concepts and some open problems.

Carlos Benítez Rodríguez (1989)

Revista Matemática de la Universidad Complutense de Madrid

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Orthogonality in inner products is a binary relation that can be expressed in many ways without explicit mention to the inner product of the space. Great part of such definitions have also sense in normed linear spaces. This simple observation is at the base of many concepts of orthogonality in these more general structures. Various authors introduced such concepts over the last fifty years, although the origins of some of the most interesting results that can be obtained for these generalized...

Topological Properties of Real Normed Space

Kazuhisa Nakasho, Yuichi Futa, Yasunari Shidama (2014)

Formalized Mathematics

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In this article, we formalize topological properties of real normed spaces. In the first part, open and closed, density, separability and sequence and its convergence are discussed. Then we argue properties of real normed subspace. Then we discuss linear functions between real normed speces. Several kinds of subspaces induced by linear functions such as kernel, image and inverse image are considered here. The fact that Lipschitz continuity operators preserve convergence of sequences...

On (a,b,c,d)-orthogonality in normed linear spaces

C.-S. Lin (2005)

Colloquium Mathematicae

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We first introduce a notion of (a,b,c,d)-orthogonality in a normed linear space, which is a natural generalization of the classical isosceles and Pythagorean orthogonalities, and well known α- and (α,β)-orthogonalities. Then we characterize inner product spaces in several ways, among others, in terms of one orthogonality implying another orthogonality.

Baire's Category Theorem and Some Spaces Generated from Real Normed Space 1

Noboru Endou, Yasunari Shidama, Katsumasa Okamura (2006)

Formalized Mathematics

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As application of complete metric space, we proved a Baire's category theorem. Then we defined some spaces generated from real normed space and discussed each of them. In the second section, we showed the equivalence of convergence and the continuity of a function. In other sections, we showed some topological properties of two spaces, which are topological space and linear topological space generated from real normed space.