Mappings and inductive invariants
Mappings covered by products and pinched products
Mappings of proximity structures
Mappings of terminal continua.
Mappings on compact metric spaces
Mappings on manifolds
Mappings on -paracompact spaces.
Mappings on the dyadic solenoid
Answering an open problem in [3] we show that for an even number , there exist no to mappings on the dyadic solenoid.
Mappings onto circle-like continua
Mappings related to confluence
Necessary and sufficient conditions are found in the paper for a mapping between continua to be monotone, confluent, semi-confluent, joining, weakly confluent and pseudo-confluent. Three lists of these conditions are presented. Two are formulated in terms of components and of quasi-components, respectively, of connected closed subsets of the range space, while the third one in terms of connectedness between subsets of the domain space. Some basic relations concerning these concepts are studied.
Mappings that preserve Cauchy sequences
Mappings with 1-dimensional absolute neighborhood retract fibers
Maps and inverse systems of metric spaces
Maps between weak solenoidal spaces
Maps of the interval Ljapunov stable on the set of nonwandering points.
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 sets in the Hashimoto topologies for measure and category
Marczewski sets, measure and the Baire property
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...
Markoff property of generalized random fields