Name
Abstract | ||
|---|---|---|
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 sub-space. 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 is also refered here. Then we argue the condition when real normed subspaces become Banach's spaces. We also formalize quotient vector space. In the last session, we argue the properties of the closure of real normed space. These formalizations are based on [19](p.3-41), [2] and [34](p.3-67). |
Year | DOI | Venue |
|---|---|---|
2014 | 10.2478/forma-2014-0024 | FORMALIZED MATHEMATICS |
Keywords | Field | DocType |
functional analysis, normed linear space, topological vector space | Topology,Discrete mathematics,Function space,Reflexive space,Normed vector space,Continuous functions on a compact Hausdorff space,Complete metric space,Mathematical analysis,Topological vector space,Strictly convex space,Normed algebra,Mathematics | Journal |
Volume | Issue | ISSN |
22 | 3 | 1898-9934 |
Citations | PageRank | References |
3 | 0.75 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kazuhisa Nakasho | 1 | 7 | 8.59 |
| Yuichi Futa | 2 | 23 | 15.08 |
| Yasunari Shidama | 3 | 166 | 72.47 |