In this paper we further a previous study concerning abstract regularity for monotone set multifunctions, with has immediate applications in well-known situations such as the Borel σ-algebra of a Hausdorff space and/or the Borel (Baire, respectively) δ-ring or σ-ring of a locally compact Hausdorff space. We also study relationships among abstract regularities and other properties of continuity....

• The conditions are investigated under which the upper Vietoris topology coincides with Scott on K ( X ) . For a well-filtered space having first-countable Smyth power space, and coincide. T 0 in set of minimal elements any compact saturated subset, its is first-countable. Alexandroff double circle, first-countable, not , let be poset all non-empty sets reverse inclusion order. said to have pr...

Following Kukie la, we show how to generalize some results from May’s book [4] concerning cores of finite spaces to cores of Alexandroff spaces. It turns out that finite space methods can be extended under certain local finiteness assumptions; in particular, every bounded-paths space or countable finite-paths space has a core, and two bounded-paths spaces or countable finite-paths spaces are ho...

A generalized ordered space (a GO-space) is a triple (X, τ,<) where (X,<) is a linearly ordered set and τ is a Hausdorff topology on X that has a base of order-convex sets. If τ is the usual open interval topology of the order <, then we say that (X, τ,<) is a linearly ordered topological space (LOTS). Besides the usual real line, probably the most familiar examples of GO-spaces are the Sorgenf...

In this paper will be presented a new maximum principle of elliptic differential equations in divergence form which can be regarded as the counterpart of the Alexandroff-Bakelman-Pucci maximum principle of elliptic differential equations in nondivergence form.

&lt;p&gt;It was demonstrated in [2] that the Alexandroff duplicate of Čech-Stone compactification naturals is not extremally disconnected. The question raised as to whether a non-discrete disconnected space can ever be We answer this affirmative; an example van Douwen significant. In slightly different direction we also characterize when P-space well it almost P-space.&lt;/p&gt;