In [5] Todorčević shows that there is no Hausdorff gap (A,B) if A is analytic. In this note we extend the result by showing that the assertion “there is no Hausdorff gap (A,B) if A is coanalytic” is equivalent to “there is no Hausdorff gap (A,B) if A is Σ2”, and equivalent to ∀r (א L[r] 1 < א1). We also consider real-valued games corresponding to Hausdorff gaps, and show that ADR for pointclass...

‎recently‎, ‎hussain et al.‎, ‎discussed the concept of $wt$-distance on a‎ ‎metric type space‎. ‎in this paper‎, ‎we prove some fixed‎ ‎point theorems for classes of contractive type multi-valued operators‎, ‎by using $wt$-distances in the setting of a complete metric type space‎. ‎these results generalize a result of feng and liu on multi-valued operators.

We introduce modal compact Hausdorff spaces as generalizations of modal spaces, and show these are coalgebras for the Vietoris functor on compact Hausdorff spaces. Modal compact regular frames and modal de Vries algebras are introduced as algebraic counterparts of modal compact Hausdorff spaces, and dualities are given for the categories involved. These extend the familiar Isbell and de Vries d...

In this work the main objective is to extend the theory of Hausdorff measures in general metric spaces. Throughout the thesis Hausdorff measures are defined using premeasures. A condition on premeasures of ‘finite order’ is introduced which enables the use of a Vitali type covering theorem. Weighted Hausdorff measures are shown to be an important tool when working with Hausdorff measures define...

In the present work we show that the linear operations in the space of Hausdorff continuous functions are generated by an extension property of these functions. We show that the supremum norm can be defined for Hausdorff continuous functions in a similar manner as for real functions, and that the space of all bounded Hausdorff continuous functions on an open set is a normed linear space. Some i...

We show that a topological space is hereditarily irresolvable if and only if it is Hausdorff-reducible. We construct a compact irreducible T1-space and a connected Hausdorff space, each of which is strongly irresolvable. Furthermore, we show that the three notions of scattered, Hausdorff-reducible, and hereditarily irresolvable coincide for a large class of spaces, including metric, locally com...

I t1 1 ⊗ · · · ⊗ tn n γ. This problem will be called the weak multilinear Hausdorff problem of moments for μk. Comparison with classical results will allow us to relate the weak multilinear Hausdorff problem with the multivariate Hausdorff problem. A solution to the strong multilinear Hausdorff problem of moments will be provided by exhibiting necessary and sufficient conditions for the existen...

OBJECTIVE To evaluate surgery results, we established a novel method to digitize nasal morphology with the use of Hausdorff distance and analyzed nose morphology after cheiloplasty. STUDY DESIGN We evaluated the naris after primary cheiloplasty of 30 unilateral cleft lip and palate patients. Similarity between left and right sides was assessed by visual evaluation, area ratio, perimeter ratio...

The set of interval Hausdorff continuous functions constitutes the largest space preserving basic algebraic and topological structural properties of continuous functions, such as linearity, ring structure, Dedekind order completeness, etc. Spaces of interval functions have important applications not only in the construction of numerical methods and algorithms, but to problems in abstract areas ...