Trapezoid maps are a kind of continuous and piecewise linear maps with a flat top. By the conjugacy relationship, we present a complete classification for four families of trapezoid maps. Firstly, using an extension method, we construct all homeomorphic solutions of conjugacy equation φ ◦ f = g ◦ φ for some non-monotone continuous maps f and g. Secondly, using an iterative construction method a...

in this paper, we have dened and studied a generalized form of topological vectorspaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of levine. along with other results, it is provedthat every s-topological vector space is generalized homogeneous space. every open subspaceof an s-topological vector space is ...

We put forward a revised definition of stably compact spaces which allows us to show their equivalence with Nachbin’s compact ordered spaces in an entirely elementary fashion. We then exhibit some constructions for stably compact spaces which apparently have not appeared in the literature before. These constructions allow us to show that the set of (sub-)probability valuations can be equipped w...

A class of skew products over irrational rotations of the circle is defined which contains some systems which have strange nonchaotic attractors. The global attractor of these systems is characterized: it lies between an upper semi-continuous curve and a lower semi-continuous curve. With additional assumptions on the class of maps considered more detail of the attractor can be given. Mathematic...

Received We show that the category whose objects are famidclies of Markov processes on Polish spaces, with a given transition kernel, and whose morphisms are transition probability preserving, surjective continuous maps has semi-pullbacks, i.e. for any pair of morphisms fi : Si ! S (i = 1; 2), there exists an object V and morphisms i : V ! Si (i = 1; 2) such that f1 1 = f2 2. This property hold...

We prove that an n-valued function that is lower semi-continuous is also upper semi-continuous and therefore continuous, that is, an n-valued map. Several conditions are shown to be equivalent to continuity for n-valued functions, in particular the continuity of a corresponding singlevalued function to a configuration space. Consequently, splitting is related to braid groups to prove a Splittin...

This article concerns the existence of solutions for fractional-order differential inclusions with boundary-value conditions. The main tools are based on fixed point theorems due to Bohnerblust-Karlin and Leray-Schauder together with a continuous selection theorem for upper semi-continuous multivalued maps.

In this paper, we characterize stratifiable (or semi-stratifiable) spaces, and monotonically countably paracompact metacompact) spaces by expansions of locally upper bounded semi-continuous poset-valued maps. These extend earlier results for real-valued Locally functions.