Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-24T10:39:12.670Z Has data issue: false hasContentIssue false

Notes on differential calculus in topological linear spaces, II

Published online by Cambridge University Press:  09 April 2009

S. Yamamuro
Affiliation:
Department of Mathematics Institute of Advanced StudiesAustralian National UniversityCanberra.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Throughout this note, let E and F be locally convex Hausdorff spaces over the real number field R. We denote real numbers by Greek letters. The sets of all continuous semi-norms on E and F will be denoted by P(E) and P(F) respectively, and A will always stand for an open subset of E.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1975

References

Bessaga, C., Pelczyński, A. and Rolewicz, S. (1961), ‘On diametral approximative dimension and linear homogeneity of F-spaces’, Bull. Acad. Polon. Sci. Sér. Math. Astronom. Phys. 9, 677683.Google Scholar
Dieudonné, J. (1960), Foundations of Modern Analysis (Academic Press, New York, 1960).Google Scholar
Keller, H. H. (19631964), ‘Differenzierbarkeit in topologischen Vektorräumen’, Comment. Math. Helv. 38, 308320.CrossRefGoogle Scholar
Suhinin, M. F. (1969), ‘Two versions of a theorem on the differentiation of the inverse function in certain linear topological space (Russian)’, Vestnik Moskow Univ. Ser. 1, 24, 3438.Google Scholar
Yamamuro, S. (to appear), ‘Notes on differential calculus in topological linear spaces’, J. Reine Angew. Math.Google Scholar
Yamamuro, S. (1974), Differential Calculus in Topological Linear Spaces, Lecture Notes in Math., Vol. 374 (Springer-Verlag, 1974).CrossRefGoogle Scholar