A characterization of locally connected continua which are quasi-embeddable into
A characterization of locally connectedness by means of the set function T
A characterization of MAR and MANR-spaces by extendability of mutations
A characterization of open mapping in terms of convergent sequences.
A characterization of pseudocompactness.
A characterization of realcompactness in terms of the topology of pointwise convergence on the function space
A characterization of regular averaging operators and its consequences
We present a characterization of continuous surjections, between compact metric spaces, admitting a regular averaging operator. Among its consequences, concrete continuous surjections from the Cantor set 𝓒 to [0,1] admitting regular averaging operators are exhibited. Moreover we show that the set of this type of continuous surjections from 𝓒 to [0,1] is dense in the supremum norm in the set of all continuous surjections. The non-metrizable case is also investigated. As a consequence, we obtain...
A characterization of the -realcompact space
A characterization of Valdivia compact spaces.
A characterization of ω-limit sets for piecewise monotone maps of the interval
For a piecewise monotone map f on a compact interval I, we characterize the ω-limit sets that are bounded away from the post-critical points of f. If the pre-critical points of f are dense, for example when f is locally eventually onto, and Λ ⊂ I is closed, invariant and contains no post-critical point, then Λ is the ω-limit set of a point in I if and only if Λ is internally chain transitive in the sense of Hirsch, Smith and Zhao; the proof relies upon symbolic dynamics. By identifying points of...
A class α and locally connected continua which can be ε-mapped onto a surface
A classification of braid types for periodic orbits of diffeomorphisms of surfaces of genus one with topological entropy zero.
We classify the braid types that can occur for finite unions of periodic orbits of diffeomorphisms of surfaces of genus one with zero topological entropy.
A classification of continua and weakly confluent mappings
A classification of H-closed extensions
A classification of separable Rosenthal compacta and its applications [Book]
A cohomological index of Fuller type for parameterized set-valued maps in normed spaces
We construct a cohomological index of the Fuller type for set-valued flows in normed linear spaces satisfying the properties of existence, excision, additivity, homotopy and topological invariance. In particular, the constructed index detects periodic orbits and stationary points of set-valued dynamical systems, i.e., those generated by differential inclusions. The basic methods to calculate the index are also presented.
A common end point theorem for set-valued generalized -weak contraction.
A Cone of Inhomogeneous Second-Order Polynomials.
A conglomerate of exponential supercategories of the category of finitely generated topological spaces.
A connection between multiplication in C(X) and the dimension of X
Let X be a compact Hausdorff topological space. We show that multiplication in the algebra C(X) is open iff dim X < 1. On the other hand, the existence of non-empty open sets U,V ⊂ C(X) satisfying Int(U· V) = ∅ is equivalent to dim X > 1. The preimage of every set of the first category in C(X) under the multiplication map is of the first category in C(X) × C(X) iff dim X ≤ 1.