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Linear Transformations of Euclidean Topological Spaces. Part II

Sat, 01 Jan 2011 00:00:00 GMT

Tytuł: Linear Transformations of Euclidean Topological Spaces. Part II Autorzy: Pąk, Karol Abstrakt: We prove a number of theorems concerning various notions used in the theory of continuity of barycentric coordinates.

Banach Algebra of Bounded Complex-Valued Functionals

Sat, 01 Jan 2011 00:00:00 GMT

Tytuł: Banach Algebra of Bounded Complex-Valued Functionals Autorzy: Kanazashi, Katuhiko; Okazaki, Hiroyuki; Shidama, Yasunari Abstrakt: In this article, we describe some basic properties of the Banach algebra which is constructed from all bounded complex-valued functionals.

The Axiomatization of Propositional Linear Time Temporal Logic

Sat, 01 Jan 2011 00:00:00 GMT

Tytuł: The Axiomatization of Propositional Linear Time Temporal Logic Autorzy: Giero, Mariusz Abstrakt: The article introduces propositional linear time temporal logic as a formal system. Axioms and rules of derivation are defined. Soundness Theorem and Deduction Theorem are proved [9].

Veblen Hierarchy

Sat, 01 Jan 2011 00:00:00 GMT

Tytuł: Veblen Hierarchy Autorzy: Bancerek, Grzegorz Abstrakt: The Veblen hierarchy is an extension of the construction of epsilon numbers (fixpoints of the exponential map: ωε = ε). It is a collection φα of the Veblen Functions where φ0(β) = ωβ and φ1(β) = εβ. The sequence of fixpoints of φ1 function form φ2, etc. For a limit non empty ordinal λ the function φλ is the sequence of common fixpoints of all functions φα where α < λ. The Mizar formalization of the concept cannot be done directly as the Veblen functions are classes (not (small) sets). It is done with use of universal sets (Tarski classes). Namely, we define the Veblen functions in a given universal set and φα(β) as a value of Veblen function from the smallest universal set including α and β.