Digitally continuous functions

Digitally Continuous Multivalued Functions

We introduce in this paper a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach uses multivalued maps. We show how the multivalued approach provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we characterize t...

Contra $beta^{*}$-continuous and almost contra $beta^{*}$-continuous functions

The notion of contra continuous functions was introduced and investigated by Dontchev. In this paper, we apply the notion of $beta^{*}$-closed sets in topological space to present and study a new class of functions called contra $beta^{*}$-continuous and almost contra $beta^{*}$-continuous functions as a new generalization of contra continuity.

Generalized Rings of Measurable and Continuous Functions

This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

Digitally Enhanced Continuous- Time Sigma-Delta Analogue-to-Digital Converters

Decomposing Symmetrically Continuous and Sierpiński-zygmund Functions into Continuous Functions

In this paper we will investigate the smallest cardinal number κ such that for any symmetrically continuous function f : R → R there is a partition {Xξ : ξ < κ} of R such that every restriction f Xξ : Xξ → R is continuous. The similar numbers for the classes of Sierpiński-Zygmund functions and all functions from R to R are also investigated and it is proved that all these numbers are equal. We ...