Mapping approximate inverse systems of compacta
Mapping theorems on countable tightness and a question of F. Siwiec
In this paper -quotient maps and -spaces are introduced. It is shown that (1) countable tightness is characterized by -quotient maps and quotient maps; (2) a space has countable tightness if and only if it is a countably bi-quotient image of a locally countable space, which gives an answer for a question posed by F. Siwiec in 1975; (3) -spaces are characterized as the -quotient images of metric spaces; (4) assuming , a compact -space is an -space if and only if every countably compact subset...
Mapping theorems on -spaces
In this paper we improve some mapping theorems on -spaces. For instance we show that an -space is preserved by a closed and countably bi-quotient map. This is an improvement of Yun Ziqiu’s theorem: an -space is preserved by a closed and open map.
Mappings and inductive invariants
Mappings of terminal continua.
Mappings on compact metric spaces
Mappings onto circle-like continua
Mappings that preserve Cauchy sequences
Maps and inverse systems of metric spaces
Maps with dimensionally restricted fibers
We prove that if f: X → Y is a closed surjective map between metric spaces such that every fiber belongs to a class S of spaces, then there exists an -set A ⊂ X such that A ∈ S and for all y ∈ Y. Here, S can be one of the following classes: (i) M: e-dim M ≤ K for some CW-complex K; (ii) C-spaces; (iii) weakly infinite-dimensional spaces. We also establish that if S = M: dim M ≤ n, then dim f ∆ g ≤ 0 for almost all .
Marczewski-Burstin-like characterizations of σ-algebras, ideals, and measurable functions
ℒ denotes the Lebesgue measurable subsets of ℝ and denotes the sets of Lebesgue measure 0. In 1914 Burstin showed that a set M ⊆ ℝ belongs to ℒ if and only if every perfect P ∈ ℒ$ℒ0 which is a subset of or misses M (a similar statement omitting “is a subset of or” characterizes ). In 1935, Marczewski used similar language to define the σ-algebra (s) which we now call the “Marczewski measurable sets” and the σ-ideal which we call the “Marczewski null sets”. M ∈ (s) if every perfect set P has...
Martin’s Axiom and -resolvability of Baire spaces
We prove that, assuming MA, every crowded space is -resolvable if it satisfies one of the following properties: (1) it contains a -network of cardinality constituted by infinite sets, (2) , (3) is a Baire space and and (4) is a Baire space and has a network with cardinality and such that the collection of the finite elements in it constitutes a -locally finite family. Furthermore, we prove that the existence of a Baire irresolvable space is equivalent to the existence of...
Maß und Kategorie von Summenmengen.
Maximal Elements in Ordered Topological Spaces
Maximal p-Systems and Realcompleteness.
Measurability of equivalence classes and MEC-property in metric spaces.
Measurable cardinals and category bases
We show that the existence of a non-trivial category base on a set of regular cardinality with each subset being Baire is equiconsistent to the existence of a measurable cardinal.
Measurable uniform spaces
Measure of noncompactness of subsets of Lebesgue spaces
Measure of nonhyperconvexity and fixed-point theorems.