This paper deals with families of conformal iterated function systems (CIFS). The space CIFS(X, I) of all CIFS, with common seed space X and alphabet I, is successively endowed with the topology of pointwise convergence and the so-called λ-topology. We show just how bad the topology of pointwise convergence is: although the Hausdorff dimension function is continuous on a dense Gδ-set, it is als...

An MI-group is an algebraic structure based on a generalization of the concept of a monoid that satisfies the cancellation laws and is endowed with an invertible anti-automorphism representing inversion. In this paper, a topology is defined on an MI-group $G$ under which $G$ is  a topological MI-group. Then we will identify open, discrete and compact MI-subgroups. The connected components of th...

the aim of the present study was to find the best or optimum topology of six chicken populations, which were genotyped based on nine highly polymorphic microsatellite markers. to reach this goal, different genetic distances based on infinite allele model (iam), stepwise mutation model (smm) and drawing phylogentic trees on un-weighted pair-group method using arithmetic averages (upgma) method w...

in this paper, we introduce λκ−closed sets and study its properties in generalized topological spaces.

in this paper, by presenting some notions and theorems, we obtaindifferent types of fuzzy topologies. in fact, we obtain somelowen-type  and chang-type fuzzy topologies on general fuzzyautomata. to this end, first we define a kuratowski fuzzy interioroperator which induces a  lowen-type  fuzzy topology on the  set ofstates of a max- min general   fuzzy automaton. also by  provingsome theorems, ...

In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices,  topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and defi...