Chains of simple closed curves and a dogbone space
Champs mesurables et multisections
Chaotic behaviour of the map x ↦ ω(x, f)
Let K(2ℕ) be the class of compact subsets of the Cantor space 2ℕ, furnished with the Hausdorff metric. Let f ∈ C(2ℕ). We study the map ω f: 2ℕ → K(2ℕ) defined as ω f (x) = ω(x, f), the ω-limit set of x under f. Unlike the case of n-dimensional manifolds, n ≥ 1, we show that ω f is continuous for the generic self-map f of the Cantor space, even though the set of functions for which ω f is everywhere discontinuous on a subsystem is dense in C(2ℕ). The relationships between the continuity of ω f and...
Chaotic continua of (continuum-wise) expansive homeomorphisms and chaos in the sense of Li and Yorke
A homeomorphism f : X → X of a compactum X is expansive (resp. continuum-wise expansive) if there is c > 0 such that if x, y ∈ X and x ≠ y (resp. if A is a nondegenerate subcontinuum of X), then there is n ∈ ℤ such that (resp. ). We prove the following theorem: If f is a continuum-wise expansive homeomorphism of a compactum X and the covering dimension of X is positive (dim X > 0), then there exists a σ-chaotic continuum Z = Z(σ) of f (σ = s or σ = u), i.e. Z is a nondegenerate subcontinuum...
Chapman's category isomorphism for arbitrary ARs
Chapman's Classification of Shapes. A Proof Using Collapsing.
Characterization of a certain subset of the Cantor set
Characterization of Baire-one functions between topological spaces
Characterization of chaos for continuous maps of the circle
Characterization of convergence in fuzzy topological spaces.
Characterization of Fourier-Stieltjes transforms of vector-valued measures
Characterization of fuzzy neighborhood commutative division rings. II.
Characterization of Hilbert cube manifolds: an alternate proof
Characterization of realcompactness and hereditary realcompactness in the class of normal nodec (submaximal) spaces
Is it true in ZFC that every normal submaximal space of non-measurable cardinality is hereditarily realcompact? This question (posed by O. T. Alas et al. (2002)) is given a complete affirmative answer, for a wider class of spaces. In fact, this answer is a part of a bi-conditional statement: A normal nodec space X is hereditarily realcompact if and only if it is realcompact if and only if every closed discrete (or nowhere dense) subset of X has non-measurable cardinality.
Characterization of strongly exposed points in .
Characterization of ultra separation axioms via -kernel.
Characterizations and Metrization of Proper Analytic Spaces.
Characterizations of absolute -sets
Characterizations of basic bitopological separation axioms
Characterizations of certain general and reproductive solutions of arbitrary equations