Abstract:
New characterizations of almost contra-precontinuity are presented. These characterizations are used to develop a new weak form of almost contra-precontinuity. This new weak form is then used to extend several results in the literature concerning almost contra-precontinuity.

Abstract:
In this paper, we apply the notion of pre-$mathcal{I}$-open sets to present and study a new class of functions called contra pre-$mathcal{I}$-continuous functions in ideal topological spaces. Relationships between this new class and other classes of functions are investigated and some characterisations of this new class of functions are studied. Also we introduce the notions of contra strong $beta$-$mathcal{I}$-continuous functions and contra $delta$-$mathcal{I}$-continuous functions to obtain decompositions of contra $alpha$-$mathcal{I}$-continuity and contra semi-$mathcal{I}$-continuity.

Abstract:
A taut foliation of a hyperbolic 3-manifold has the continuous extension property for leaves in almost every direction; that is, for each leaf of the universal cover of the foliation and almost every geodesic ray in the leaf, the limit of the ray in the universal cover of the 3-manifold is a well-defined point in the ideal boundary.

Abstract:
The purpose of this paper is to introduce a new class of functions called almost ps-continuous function by using ps-open sets in topological spaces. Some properties and characterizations of this function are given.

Abstract:
In this paper, a new class of functions called “almost 3-continuous ” is introduced and their several properties are investigated. This new class is also utilized to improve some published results concerning weak continuity [6] and 3-continuity [2].

Abstract:
In this paper we prove that, in the space ° ’ of almost continuous functions (with the metric of uniform convergence), the set of functions of the first class of Baire is superporous at each point of this space

Abstract:
We prove an almost continuous version of Dye's theorem: any two non-atomic probability measure preserving homeomorphisms of Polish spaces are almost continuously orbit equivalent. More precisely they are orbit equivalent by a map which is defined and continuous on a Polish subset of full measure with an inverse satisfying the same conditions. This result includes all of the recent results on almost continuous orbit equivalence. We also deal with the case of infinite invariant measures.

Abstract:
M. K. Singal and Asha Rani Singal have defined an almost-continuous function f:X ￠ ’Y to be one in which for each x ￠ X and each regular-open set V containing f(x), there exists an open U containing x such that f(U) ￠ V. A space Y may now be defined to be almost-continuous path connected if for each y0,y1 ￠ Y there exists an almost-continuous f:I ￠ ’Y such that f(0)=y0 and f(1)=y1 An investigation of these spaces is made culminating in a theorem showing when the almost-continuous path connected components coincide with the usual components of Y.

Abstract:
We prove that the spectrum of the almost Mathieu operator is absolutely continuous if and only if the coupling is subcritical. This settles Problem 6 of Barry Simon's list of Schr\"odinger operator problems for the twenty-first century.

Abstract:
We prove that every semi-continuous function on a metrizable space is decompose into sum of two quasi-continuous functions. And then we obtain a new characterization of the oscillation of almost continuous functions.