In this note we obtain necessary and sufficient conditions for a convergence space to have a smallest Hausdorff compactification and to have a smallest regular compactification. Introduction. A Hausdorff convergence space as defined in [1] always has a Stone-Cech compactification which can be obtained by a slight modification of the result in [3]. But in general this need not be the largest Hau...

In the study of fixed points of an operator it is useful to consider a more general concept, namely coupled fixed point. Edit In this paper, by using notion partial metric, we introduce a metric space $S$-Hausdorff on the set of all close and bounded subset of $X$. Then the fixed point results of multivalued continuous and surjective mappings are presented. Furthermore, we give a positive resul...

In this paper, we derive some identities for the Hausdorff measures of noncompactness of certain matrix operators on the sequence spaces X(r,s) of generalized means. Further, we apply the Hausdorff measure of noncompactness to obtain the necessary and sufficient conditions for such operators to be compact. Mathematics subject classification (2010): 46B15, 46B45, 46B50.

It is well known that, when endowed with the Gromov-Hausdorff distance dGH, collection M of all isometry classes compact metric spaces a complete and separable space. also that (M,dGH) geodesic space, but there no structural characterization geodesics in M. In this paper we provide two characterizations We call γ:[0,1]→M Hausdorff-realizable if exists space Z containing isometric copies γ(t) fo...

A new model of coherent upper conditional prevision is proposed in a metric space. It is defined by the Choquet integral with respect to the s-dimensional Hausdorff outer measure if the conditioning event has positive and finite Hausdorff outer measure in its dimension s. Otherwise if the conditioning event has Hausdorff outer measure in its dimension equal to zero or infinity it is defined by ...

We prove that the number of nodal points on an $\mathcal{S}$-good real analytic curve $\mathcal{C}$ a sequence $\mathcal{S}$ Laplace eigenfunctions $\varphi_j$ eigenvalue $-\lambda^2_j$ Riemannian manifold $(M, g)$ is bounded above by $A_{g , \mathcal{C}} \lambda_j$. Moreover, we codimension-two Hausdorff measure $\mathcal{H}^{m-2} (\mathcal{N}_{\varphi \lambda} \cap H)$ intersections with conn...

Generalising Nachbin's theory of ``topology and order'', in this paper we   continue the study of quantale-enriched categories equipped with a compact   Hausdorff topology. We compare these $V$-categorical compact Hausdorff spaces   with ultrafilter-quantale-enriched categories, and show that the presence of a   compact Hausdorff topology guarantees Cauchy completeness and (suitably   defined) ...

The symmetric inverse semigroup I(X) on a set X is the collection of all partial bijections between subsets with composition as algebraic operation. We study minimal Hausdorff topology I(X). present some characterizations it. When countable such Polish.