منابع مشابه
Real Recursive Functions and Baire Classes
Recursive functions over the reals [6] have been considered, first as a model of analog computation, and second to obtain analog characterizations of classical computational complexity classes [2]. However, one of the operators introduced in the seminal paper by Cris Moore (in 1996), the minimalization operator, creates some difficulties: (a) although differential recursion (the analog counterp...
متن کاملBaire Categories on Small Complexity Classes and Meager-Comeager Laws
We introduce two resource-bounded Baire category notions on small complexity classes such as P, QUASIPOLY, SUBEXP and PSPACE and on probabilistic classes such as BPP, which differ on how the corresponding finite extension strategies are computed. We give an alternative characterization of small sets via resource-bounded Banach-Mazur games. As an application of the first notion, we show that for...
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Certain subclasses of B 1 (K), the Baire-1 functions on a compact metric space K, are defined and characterized. Some applications to Banach spaces are given. Let X be a separable infinite dimensional Banach space and let K denote its dual ball, Ba(X *), with the weak* topology. K is compact metric and X may be naturally identified with a closed subspace of C(K). X * * may also be identified wi...
متن کاملOn the Baire Category Theorem
Let T be a topological structure and let A be a subset of the carrier of T . Then IntA is a subset of T . Let T be a topological structure and let P be a subset of the carrier of T . Let us observe that P is closed if and only if: (Def. 1) −P is open. Let T be a non empty topological space and let F be a family of subsets of T . We say that F is dense if and only if: (Def. 2) For every subset X...
متن کاملQuestions on generalised Baire spaces
When studying questions about real numbers, it is common practice in set theory to investigate the closely related Baire space ω and Cantor space 2 . These spaces have been extensively studied by set theorists from various points of view, e.g., questions about cardinal characteristics of the continuum, descriptive set theory and other combinatorial questions. Furthermore, the investigation of 2...
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky
سال: 1970
ISSN: 0528-2195
DOI: 10.21136/cpm.1970.117693