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Nondiscrete mathematical induction and iterative existence proofs. (English) Zbl 0323.46005

MSC:
46A30 Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
46B99 Normed linear spaces and Banach spaces; Banach lattices
47H10 Fixed-point theorems
03F99 Proof theory and constructive mathematics
46A19 Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \(\mathbb{R}\), etc.)
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References:
[1] Pták, V., A theorem of the closed graph type, Manuscr. math., 13, 109-130, (1974) · Zbl 0286.46008
[2] Pták, V., Deux théorèmes de factorisation, C. R. acad. sci. (Paris), 278, 1091-1094, (1974) · Zbl 0277.46047
[3] Pták, V., A quantitative refinement of the closed graph theorem, Czech. math. J., 99, 503-506, (1974) · Zbl 0315.46007
[4] Pták, V., On the closed graph theorem, Czech. math. J., 84, 523-527, (1959) · Zbl 0093.12002
[5] Křížková, J.; Vrbová, P., A remark on a factorization theorem, Commeutationes math. univ. carolinae, 15, 611-614, (1974) · Zbl 0329.46055
[6] Zemánek, J., A remark on transitivity of operator algebras, Čas. Pěst. mat., 100, 176-178, (1975) · Zbl 0302.46044
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