Component restriction property for classes of mappings.
Compositions of simple maps
A map (= continuous function) is of order ≤ k if each of its point-inverses has at most k elements. Following [4], maps of order ≤ 2 are called simple. Which maps are compositions of simple closed [open, clopen] maps? How many simple maps are really needed to represent a given map? It is proved herein that every closed map of order ≤ k defined on an n-dimensional metric space is a composition of (n+1)k-1 simple closed maps (with metric domains). This theorem fails to be true...
Concerning a problem due to Sam B. Nadler, Jr.
Connected economically metrizable spaces
A topological space is non-separably connected if it is connected but all of its connected separable subspaces are singletons. We show that each connected sequential topological space X is the image of a non-separably connected complete metric space X under a monotone quotient map. The metric of the space X is economical in the sense that for each infinite subspace A ⊂ X the cardinality of the set does not exceed the density of A, . The construction of the space X determines a functor : Top...
Continua determined by mappings.
Continuous decompositions of Peano plane continua into pseudo-arcs
Locally planar Peano continua admitting continuous decomposition into pseudo-arcs (into acyclic curves) are characterized as those with no local separating point. This extends the well-known result of Lewis and Walsh on a continuous decomposition of the plane into pseudo-arcs.
Contractions over generalized metric spaces.
Covering Properties of Continua and Mappings
Cyclic Type Fixed Point Results in 2-Menger Spaces
In this paper we introduce generalized cyclic contractions through number of subsets of a probabilistic 2-metric space and establish two fixed point results for such contractions. In our first theorem we use the Hadzic type -norm. In another theorem we use a control function with minimum -norm. Our results generalizes some existing fixed point theorem in 2-Menger spaces. The results are supported with some examples.
Dendrites and monotone mappings.
Descriptive properties of mappings between nonseparable Luzin spaces
We relate some subsets of the product of nonseparable Luzin (e.g., completely metrizable) spaces to subsets of in a way which allows to deduce descriptive properties of from corresponding theorems on . As consequences we prove a nonseparable version of Kondô’s uniformization theorem and results on sets of points in with particular properties of fibres of a mapping . Using these, we get descriptions of bimeasurable mappings between nonseparable Luzin spaces in terms of fibres.
Eigentlich operierende Gruppen von Isometrien
Equivalent contractive conditions in metric spaces.
Erweiterung einer stetigen Abbildung
Every graph is a self-similar set.
Extension and reconstruction theorems for the Urysohn universal metric space
We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. As an application, we prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.
Extensions of Ćirić generalised contractions
Extensions of compact continuous maps into decomposable sets
Extensions of nonexpansive mappings in the Hilbert ball with the hyperbolic metric. I.
Extensions of nonexpansive mappings in the Hilbert ball with the hyperbolic metric. II.