We study the multi-dimensional re ection map on the spaces D([0; T ];Rk ) and D([0;1);Rk ) of right-continuous Rk -valued functions on [0; T ] or [0;1) with left limits, endowed with variants of the Skorohod(1956) M1 topology. The re ection map was used with the continuous mapping theorem by Harrison and Reiman (1981) and Reiman (1984) to establish heavy-tra c limit theorems with re ected Brown...

In this paper, we prove that into isometries and disjointness preserving linear maps from C0(X) into C0(Y ) are essentially weighted composition operators Tf = h · f ◦ φ for some continuous map φ and some continuous scalar-valued function h.

In this paper, we prove that into isometries and disjointness preserving linear maps from C0(X) into C0(Y ) are essentially weighted composition operators Tf = h · f ◦ φ for some continuous map φ and some continuous scalar-valued function h.

BACKGROUND For a majority of patients undergoing anaesthesia for general surgery, mean arterial pressure (MAP) is only measured intermittently by arm cuff oscillometry (MAPiNIAP). In contrast, the Nexfin(®) device provides continuous non-invasive measurement of MAP (MAPcNIAP) using a finger cuff. We explored the agreement of MAPcNIAP and MAPiNIAP with the gold standard: continuous invasive MAP ...

Suppose that the inverse image of the zero vector by a continuous map f : R → R has an isolated point P . The existence of a continuous map g which approximates f but is nonvanishing near P is equivalent to a topological property we call “locally inessential,” generalizing the notion of index zero for vector fields, the q = n case. For dimensions n, q where πn−1(Sq−1) is trivial, every isolated...

The scaling function of a one-dimensional Markov map is defined and studied. We prove that the scaling function of a non-critical geometrically finite one-dimensional map is Hölder continuous, while the scaling function of a critical geometrically finite one-dimensional map is discontinuous. We prove that scaling functions determine Lipschitz conjugacy classes, and moreover, that the scaling fu...

Any continuous, transitive, piecewise monotonic map is determined up to a binary choice by its dimension module with the associated finite sequence of generators. The dimension module by itself determines the topological entropy of any transitive piecewise monotonic map, and determines any transitive unimodal map up to conjugacy. For a transitive piecewise monotonic map which is not essentially...

We give a description of a weakly continuous rank preserving map on a reflexive algebra on complex Hilbert space with commutative completely distributive subspace lattice. We show that the implementation of a rank preserving map can be described by the combination of two different types of maps. We also show that a rank preserving map can be implemented by only one type if the corresponding lat...

Any continuous, transitive, piecewise monotonic map is determined up to a binary choice by its dimension module with the associated finite sequence of generators. The dimension module by itself determines the topological entropy of any transitive piecewise monotonic map, and determines any transitive unimodal map up to conjugacy. For a transitive piecewise monotonic map which is not essentially...

a topoframe, denoted by $l_{ tau}$,  is a pair $(l, tau)$ consisting of a frame $l$ and a subframe $ tau $ all of whose elements are complementary elements in$l$. in this paper, we define and study the notions of a$tau $-real-continuous function on a frame $l$ and the set of realcontinuous functions $mathcal{r}l_tau $ as an $f$-ring.we show that $mathcal{r}l_{ tau}$is actually a generalization ...