The aim of this paper is to extend the truth value table oflattice-valued convergence spaces to a more general case andthen to use it to introduce and study the quantale-valued fuzzy Scotttopology in fuzzy domain theory. Let $(L,*,varepsilon)$ be acommutative unital quantale and let $otimes$ be a binary operationon $L$ which is distributive over nonempty subsets. The quadruple$(L,*,otimes,varep...

Topology is a classical branch of mathematics, born essentially from Euler’s studies in the XVII century, which deals with abstract notion shape and geometry. Last decades were characterized by renewed interest topology topology-based tools, due to birth computational topological data analysis (TDA). A large novel family methods algorithms computing features descriptors (e.g., persistent homolo...

The Vibrio splendidus clade is the biggest in Vibrionales composed of 11 described species (25). Diversification of these species may have occurred 260 million years ago. The main driving forces of speciation in this clade have never been studied. Population biological parameters (population base recombination rate (ρ), population base mutation rate (θ), and index of association (Ia)) were dete...

Abstract In this chapter we briefly introduce important concepts from homology theory and highlight how some results Chap. 3 can be understood through the lens of algebraic topology. This accumulates in showing that Euler characteristic by means CW complexes, or intersection theory.

Abstract This chapter presents the main general topological tools, as used in later parts. In particular we highlight manifolds, homotopies and retractions.