Concerning almost realcompactifications
Conditions under which the least compactification of a regular continuous frame is perfect
We characterize those regular continuous frames for which the least compactification is a perfect compactification. Perfect compactifications are those compactifications of frames for which the right adjoint of the compactification map preserves disjoint binary joins. Essential to our characterization is the construction of the frame analog of the two-point compactification of a locally compact Hausdorff space, and the concept of remainder in a frame compactification. Indeed, one of the characterizations...
Constrained optimization: A general tolerance approach
To overcome the somewhat artificial difficulties in classical optimization theory concerning the existence and stability of minimizers, a new setting of constrained optimization problems (called problems with tolerance) is proposed using given proximity structures to define the neighbourhoods of sets. The infimum and the so-called minimizing filter are then defined by means of level sets created by these neighbourhoods, which also reflects the engineering approach to constrained optimization problems....
Constructing Banaschewski compactification without Dedekind completeness axiom.
Construction of right topological compactifications for discrete versions of subsemigroups of compact groups.
Convergence of conditional expectations for unbounded closed convex random sets
We discuss here several types of convergence of conditional expectations for unbounded closed convex random sets of the form where is a decreasing sequence of sub-σ-algebras and is a sequence of closed convex random sets in a separable Banach space.
Convergent sequences in
Coronas of ultrametric spaces
We show that, under CH, the corona of a countable ultrametric space is homeomorphic to . As a corollary, we get the same statements for the Higson’s corona of a proper ultrametric space and the space of ends of a countable locally finite group.
Countable-points compactifications for metric spaces
Countably compact spaces all countable subsets of which are scattered
Countably z-compact spaces
In this work we study countably z-compact spaces and z-Lindelof spaces. Several new properties of them are given. It is proved that every countably z-compact space is pseuodocompact (a space on which every real valued continuous function is bounded). Spaces which are countably z-compact but not countably compact are given. It is proved that a space is countably z-compact iff every countable z-closed set is compact. Characterizations of countably z-compact and z-Lindelof spaces by multifunctions...
Cp-movable at infinity spaces, compact ANR divisors and property UVWn.