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...