Hypographs of Upper Semi-continuous Maps and Continuous Maps on a Bounded Open Interval

Semi-θ-Open Sets and New Classes of Maps

R-semi-generalized Fuzzy Continuous Maps

In this paper, we introduce the concepts of r-semigeneralized fuzzy closed sets, r-semi-generalized fuzzy open sets, rsemi-generalized fuzzy continuous maps in fuzzy topological spaces and investigate some of their properties.

On the pointfree counterpart of the local definition of classical continuous maps

The familiar classical result that a continuous map from a space $X$ to a space $Y$ can be defined by giving continuous maps $varphi_U: U to Y$ on each member $U$ of an open cover ${mathfrak C}$ of $X$ such that $varphi_Umid U cap V = varphi_V mid U cap V$ for all $U,V in {mathfrak C}$ was recently shown to have an exact analogue in pointfree topology, and the same was done for the familiar cla...

Continuous Cofinal Maps on Ultrafilters

An ultrafilter U on a countable base set B has continuous Tukey reductions if whenever an ultrafilter V is Tukey reducible to U , then every monotone cofinal map f : U → V is continuous with respect to the Cantor topology, when restricted to some cofinal subset of U . We show that the slightly stronger property of having basic Tukey reductions is inherited under Tukey reducibility. It follows t...

Roots of Continuous Piecewise Monotone Maps of an Interval

We shall consider slightly more general problems. Namely, we shall investigate the existence of continuous: piecewise monotone, piecewise strictly monotone, and piecewise linear n-th roots of interval maps which have a continuous n-th root. Here by an n-th root of f we mean a map g such that f = g (g is the n-th iterate of g). A continuous map f : I → J , where I, J are closed intervals, is pie...