The boundedness principle in ordinal recursion

THE UNIFORM BOUNDEDNESS PRINCIPLE IN FUZZIFYING TOPOLOGICAL LINEAR SPACES

The main purpose of this study is to discuss the uniform boundednessprinciple in fuzzifying topological linear spaces. At first theconcepts of uniformly boundedness principle and fuzzy equicontinuousfamily of linear operators are proposed, then the relations betweenfuzzy equicontinuous and uniformly bounded are studied, and with thehelp of net convergence, the characterization of fuzzyequiconti...

Ordinal Recursion Theory

Uniform Boundedness Principle

The following two propositions are true: (1) For every sequence s1 of real numbers and for every real number r such that s1 is bounded and 0 ≤ r holds lim inf(r s1) = r · lim inf s1. (2) For every sequence s1 of real numbers and for every real number r such that s1 is bounded and 0 ≤ r holds lim sup(r s1) = r · lim sup s1. Let X be a real Banach space. One can verify that MetricSpaceNormX is co...

Ordinal machines and admissible recursion theory

We generalize standard Turing machines working in time ω on a tape of length ω to abstract machines with time α and tape length α, for α some limit ordinal. This model of computation determines an associated computability theory: α-computability theory. We compare the new theory to α-recursion theory, which was developed by G. Sacks and his school. For α an admissible ordinal, the basic notions...

Uniform Boundedness Principle for operators on hypervector spaces

The aim of this paper is to prove the Uniform Boundedness Principle and Banach-Steinhaus Theorem for anti linear operators and hence strong linear operators on Banach hypervector spaces. Also we prove the continuity of the product operation in such spaces.