We construct a family of spaces with “nice” structure which is universal in the class of all compact metrizable spaces of large transfinite dimension ω0, or, equivalently, of small transfinite dimension ω0; that is, the family consists of compact metrizable spaces whose transfinite dimension is ω0, and every compact metrizable space with transfinite dimension ω0 is embeddable in a space of the ...

We prove a formula for the Fekete-Leja transfinite diameter of the pullback of a set E ⊂ C by a regular polynomial map F , expressing it in terms of the resultant of the leading part of F and the transfinite diameter of E. We also establish the nonarchimedean analogue of this formula. A key step in the proof is a formula for the transfinite diameter of the filled Julia set of F .

We give a characterisation of an extension of the Kleene-Kreisel continuous functionals to objects of transfinite types using limit spaces of transfinite types.

Let (X,≤) be a non-empty strictly inductive poset, that is, a non-empty partially ordered set such that every non-empty chain Y has a least upper bound lub(Y ) ∈ X , a chain being a subset of X totally ordered by ≤. We are interested in sufficient conditions such that, given an element a0 ∈ X and a function f : X → X , there is some ordinal k such that ak+1 = ak, where ak is the transfinite seq...

In the beginning of article we show some consequences of the regularity axiom. In the second part we introduce the successor of a set and the notions of transitivity and connectedness wrt membership relation. Then we define ordinal numbers as transitive and connected sets, and we prove some theorems of them and of their sets. Lastly we introduce the concept of a transfinite sequence and we show...

In Chapter 8 of the book, “Graphs and Networks: Transfinite and Nonstandard,” (published by Birkhauser-Boston in 2004), nonstandard versions of transfinite graphs and of electrical networks having such graphs were defined and examined but only for the first two ranks, 0 and 1, of transfiniteness. In the present work, these results are extended to higher ranks of transfiniteness. Such is done in...

A moving finite element-based inverse method for determining the temperature on a moving surface is developed. The moving mesh is generated employing the transfinite mapping technique. The proposed algorithms are used in the estimation of surface temperature on a moving boundary with high velocity in the burning process of a homogenous low thermal diffusivity solid fuel. The measurements obtain...