Statistical convergence of subsequences of a given sequence.
Statistical convergence of subsequences of a given sequence
This paper is closely related to the paper of Harry I. Miller: Measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc. 347 (1995), 1811–1819 and contains a general investigation of statistical convergence of subsequences of an arbitrary sequence from the point of view of Lebesgue measure, Hausdorff dimensions and Baire’s categories.
Structural properties of endofunctors
Tensor products in the category of graphs
The colimits in the generalized algebraic categories
The point of the empty set
When the product-preserving functors preserve limits
-bicomplete categories and parity games
For an arbitrary category, we consider the least class of functors containing the projections and closed under finite products, finite coproducts, parameterized initial algebras and parameterized final coalgebras, i.e. the class of functors that are definable by -terms. We call the category -bicomplete if every -term defines a functor. We provide concrete examples of such categories and explicitly characterize this class of functors for the category of sets and functions. This goal is achieved...
μ-Bicomplete Categories and Parity Games
For an arbitrary category, we consider the least class of functors containing the projections and closed under finite products, finite coproducts, parameterized initial algebras and parameterized final coalgebras, i.e. the class of functors that are definable by μ-terms. We call the category μ-bicomplete if every μ-term defines a functor. We provide concrete examples of such categories and explicitly characterize this class of functors for the category of sets and functions. This goal is achieved...
Категория конечных множеств и декартово замкнутые категории
Характеризация категории линейно упорядоченных множеств.