Hyperspaces of infinite-dimensional compacta
Hyperspaces of noncompact metric spaces
Hyperspaces of Peano continua are Hubert cubes
Hyperspaces of Peano continua of euclidean spaces
If X is a space then L(X) denotes the subspace of C(X) consisting of all Peano (sub)continua. We prove that for n ≥ 3 the space is homeomorphic to , where B denotes the pseudo-boundary of the Hilbert cube Q.
Hyperspaces of polyhedra are Hilbert cubes
Hyperspaces of Proximity Spaces.
Hyperspaces of two-dimensional continua
Let X be a compact metric space and let C(X) denote the space of subcontinua of X with the Hausdorff metric. It is proved that every two-dimensional continuum X contains, for every n ≥ 1, a one-dimensional subcontinuum with . This implies that X contains a compact one-dimensional subset T with dim C (T) = ∞.
Hyperspaces of universal curves and 2-cells are true -sets
It is shown that the following hyperspaces, endowed with the Hausdorff metric, are true absolute -sets: (1) ℳ ²₁(X) of Sierpiński universal curves in a locally compact metric space X, provided ℳ ²₁(X) ≠ ∅ ; (2) ℳ ³₁(X) of Menger universal curves in a locally compact metric space X, provided ℳ ³₁(X) ≠ ∅ ; (3) 2-cells in the plane.
Hyperspaces of various locally connected ѕubcontinua
Hyperspaces where convergence to a calm limit implies eventual shape equivalence
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...
Indecomposable continua with one and two composants
Induced almost continuous functions on hyperspaces
For a metric continuum X, let C(X) (resp., ) be the hyperspace of subcontinua (resp., nonempty closed subsets) of X. Let f: X → Y be an almost continuous function. Let C(f): C(X) → C(Y) and be the induced functions given by and . In this paper, we prove that: • If is almost continuous, then f is continuous. • If C(f) is almost continuous and X is locally connected, then f is continuous. • If X is not locally connected, then there exists an almost continuous function f: X → [0,1] such that...
Induced near-homeomorphisms
We construct examples of mappings and between locally connected continua such that and are near-homeomorphisms while is not, and is a near-homeomorphism, while and are not. Similar examples for refinable mappings are constructed.
Inducing approximations homotopic to maps between inverse limits
Inductive dimensions of the inverse limit spaces
Initial Morphisms and Monomorphisms.
Invariant semiuniformities in coset spaces
Inverse limit spaces defined by only finitely many distinct bonding maps
Inverse limits and hyperspaces