Tolerances, covering systems, and the axiom of choice
Tolerances on -lattices
Topological difference posets
Topological dynamics of unordered Ramsey structures
We investigate the connections between Ramsey properties of Fraïssé classes and the universal minimal flow of the automorphism group of their Fraïssé limits. As an extension of a result of Kechris, Pestov and Todorcevic (2005) we show that if the class has finite Ramsey degree for embeddings, then this degree equals the size of . We give a partial answer to a question of Angel, Kechris and Lyons (2014) showing that if is a relational Ramsey class and is amenable, then admits a unique invariant...
Topological Interpretation of Rough Sets
Rough sets, developed by Pawlak, are an important model of incomplete or partially known information. In this article, which is essentially a continuation of [11], we characterize rough sets in terms of topological closure and interior, as the approximations have the properties of the Kuratowski operators. We decided to merge topological spaces with tolerance approximation spaces. As a testbed for our developed approach, we restated the results of Isomichi [13] (formalized in Mizar in [14]) and...
Topological model theory with an interior operator: consistency properties and back - and forth arguments.
Topological Properties of Real Normed Space
In this article, we formalize topological properties of real normed spaces. In the first part, open and closed, density, separability and sequence and its convergence are discussed. Then we argue properties of real normed subspace. Then we discuss linear functions between real normed speces. Several kinds of subspaces induced by linear functions such as kernel, image and inverse image are considered here. The fact that Lipschitz continuity operators preserve convergence of sequences is also refered...
Topological properties of the real numbers object in a topos
Topological representation for monadic implication algebras
In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.
Topological spaces compact with respect to a set of filters
If is a family of filters over some set I, a topological space X is sequencewise -compact if for every I-indexed sequence of elements of X there is such that the sequence has an F-limit point. Countable compactness, sequential compactness, initial κ-compactness, [λ; µ]-compactness, the Menger and Rothberger properties can all be expressed in terms of sequencewise -compactness for appropriate choices of . We show that sequencewise -compactness is preserved under taking products if and only if there...
Topological Structures On Classes I
Topological structures on classes I.
Topological Structures On Classes II
Topological structures on classes II.
Topological types of fewnomials
Topologically invariant σ-ideals on Euclidean spaces
We study and classify topologically invariant σ-ideals with an analytic base on Euclidean spaces, and evaluate the cardinal characteristics of such ideals.
Topologies, continuity and bisimulations
Topologies, Continuity and Bisimulations
The notion of a bisimulation relation is of basic importance in many areas of computation theory and logic. Of late, it has come to take a particular significance in work on the formal analysis and verification of hybrid control systems, where system properties are expressible by formulas of the modal μ-calculus or weaker temporal logics. Our purpose here is to give an analysis of the concept of bisimulation, starting with the observation that the zig-zag conditions are suggestive of some...
Topologies in atomic quantum logics
Topologies on quantum logics induced by measures