and -convergence in topological spaces
We extend the idea of -convergence and -convergence of sequences to a topological space and derive several basic properties of these concepts in the topological space.
-Lindelöf spaces.
Ideal Banach category theorems and functions
Based on some earlier findings on Banach Category Theorem for some “nice” -ideals by J. Kaniewski, D. Rose and myself I introduce the operator ( stands for “heavy points”) to refine and generalize kernel constructions of A. H. Stone. Having obtained in this way a generalized Kuratowski’s decomposition theorem I prove some characterizations of the domains of functions having “many” points of -continuity. Results of this type lead, in the case of the -ideal of meager sets, to important statements...
Ideal convergence and divergence of nets in -groups
In this paper we introduce the - and -convergence and divergence of nets in -groups. We prove some theorems relating different types of convergence/divergence for nets in -group setting, in relation with ideals. We consider both order and -convergence. By using basic properties of order sequences, some fundamental properties, Cauchy-type characterizations and comparison results are derived. We prove that -convergence/divergence implies -convergence/divergence for every ideal, admissible for...
Ideal equivalences for almost real-compact spaces
Ideal independence, free sequences, and the ultrafilter number
We make use of a forcing technique for extending Boolean algebras. The same type of forcing was employed in Baumgartner J.E., Komjáth P., Boolean algebras in which every chain and antichain is countable, Fund. Math. 111 (1981), 125–133, Koszmider P., Forcing minimal extensions of Boolean algebras, Trans. Amer. Math. Soc. 351 (1999), no. 8, 3073–3117, and elsewhere. Using and modifying a lemma of Koszmider, and using CH, we obtain an atomless BA, such that , answering questions raised by Monk...
Ideal version of Ramsey's theorem
We consider various forms of Ramsey's theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem which are connected with ideals of subsets of natural numbers. We characterize ideals with properties considered. We show that, in a sense, Ramsey's theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem characterize the same class of ideals. We use our results to show some versions of density Ramsey's theorem (these are similar to generalizations shown in [P....
Idealization of some topological concepts.
Ideals induced by Tsirelson submeasures
We use Tsirelson’s Banach space ([2]) to define an P-ideal which refutes a conjecture of Mazur and Kechris (see [12, 9, 8]).
Ideals of operators on Banach spaces and nuclear locally convex spaces
Ideals of the Stone-Cech compactification of semigroups.
Ideals of uniformly continuous mappings on pseudometric spaces
Idealtopologien auf geordneten Mengen
Idempotents of compact monothetic semiclosure semigroups
Identifying and distinguishing various varieties of abelian topological groups [Book]
Identifying Hilbert cubes: general methods and their application to hyperspaces by Schori and West
If it looks and smells like the reals...
Given a topological space ⟨X,T⟩ ∈ M, an elementary submodel of set theory, we define to be X ∩ M with topology generated by U ∩ M:U ∈ T ∩ M. We prove that if is homeomorphic to ℝ, then . The same holds for arbitrary locally compact uncountable separable metric spaces, but is independent of ZFC if “local compactness” is omitted.
Images of arcs - a nonseparable version of the Hahn-Mazurkiewicz theorem
Images of B(k)
Images of Borel sets and k-analytic sets