On two questions of the theory of retracts.
On two recurrence problems
We review some aspects of recurrence in topological dynamics and focus on two open problems. The first is an old one concerning the relation between Poincaré and Birkhoff recurrence; the second, due to the first author, is about moving recurrence. We provide a partial answer to a topological version of the moving recurrence problem.
On two theorems of Dyer
On two theorems of V. V. Filippov
On two-to-one continuous functions [Book]
On two-to-one functions
On Typical Compact Convex Sets in Hilbert Spaces
Let E be an infinite dimensional separable space and for e ∈ E and X a nonempty compact convex subset of E, let qX(e) be the metric antiprojection of e on X. Let n ≥ 2 be an arbitrary integer. It is shown that for a typical (in the sence of the Baire category) compact convex set X ⊂ E the metric antiprojection qX(e) has cardinality at least n for every e in a dense subset of E.
On typical parametrizations of finite-dimensional compacta on the Cantor set
We prove that if X is a perfect finite-dimensional compactum, then for almost every continuous surjection of the Cantor set onto X, the set of points of maximal order is uncountable. Moreover, if X is a perfect compactum of positive finite dimension then for a typical parametrization of X on the Cantor set, the set of points of maximal order is homeomorphic to the product of the rationals and the Cantor set.
On U-equivalence spaces
In this paper induced U-equivalence spaces are introduced and discussed. Also the notion of U- equivalently open subsets of a U-equivalence space and U-equivalently open functions are studied. Finally, equivalently uniformisable topological spaces are considered.
On ultraconnected spaces.
On ultrametric space.
On uncountable collections of continua and their span
We prove that if the Euclidean plane contains an uncountable collection of pairwise disjoint copies of a tree-like continuum X, then the symmetric span of X is zero, sX = 0. We also construct a modification of the Oversteegen-Tymchatyn example: for each ε > 0 there exists a tree such that σX < ε but X cannot be covered by any 1-chain. These are partial solutions of some well-known problems in continua theory.
On uncountable unions and intersections of measurable sets.
On unified theory for continuities.
On uniform approximation of bounded approximately continuous functions by differences of lower semicontinuous and approximately continuous ones
On uniform connectedness.
On uniform connection properties
On uniform paracompactness
On uniform paracompactness of the -metric spaces
Gli spazi -metrici uniformemente numerabilmente paracompatti sono uniformemente paracompatti. Si fornisce altresì una caratterizzazione degli spazi -metrici fini.
On uniform spaces