Decompositions of $NAB$-continuity and nano weak $AB$-continuity

Decompositions of Continuity via Ζ−open Sets

Al-Hawary [1] introduced and explored the class of ζ−open sets which is strictly weaker than open and proved that the collection of all ζ−open subsets of a space forms a topology that is finer than the original one. In this paper, we introduce what we call ζ−continuity and ζX−continuity and we give several characterizations and two decompositions of ζ−continuity. Finally, new decompositions of ...

Weak continuity with structural constraints

Nonlinear regression and nonlinear regularization are two powerful approaches to segmentation and nonlinear filtering. In this correspondence, we propose a hybrid approach that effectively combines the best of both worlds and can be efficiently implemented via the Viterbi algorithm.

Weak Forms of Continuity and Associated Properties

Markovian Bridges: Weak continuity and pathwise constructions

A Markovian bridge is a probability measure taken from a disintegration of the law of an initial part of the path of a Markov process given its terminal value. As such, Markovian bridges admit a natural parameterization in terms of the state space of the process. In the context of Feller processes with continuous transition densities, we construct by weak convergence considerations the only ver...

Properties of Some Weak Forms of Continuity

As weak forms of continuity in topological spaces, weak continuity [I], quasi continuity [2], semi continuity [3] and almost continuity in the sense of Husain [4] are well-known. Recently, the following four weak forms of continuity have been introduced: weak quasi continuity [5], faint continuity [6], subweak continuity [7] and almost weak continuity [8]. These four weak forms of continuity ar...