In this paper, the concept of countably near PS-compactness inL-topological spaces is introduced, where L is a completely distributive latticewith an order-reversing involution. Countably near PS-compactness is definedfor arbitrary L-subsets and some of its fundamental properties are studied.

In the absence of the Axiom of Choice, the “small” cardinal ω1 can exhibit properties more usually associated with large cardinals, such as strong compactness and supercompactness. For a local version of strong compactness, we say that ω1 is Xstrongly compact (where X is any set) if there is a fine, countably complete measure on ℘ω1(X). Working in ZF + DC, we prove that the ℘(ω1)-strong compact...

A metric space is said to be locally non-compact if every neighborhood contains a sequence that is bounded away from every element of the space, hence contains no accumulation point. We show within recursive mathematics that a nonvoid complete metric space is locally non-compact iff it is without isolated points. The result has an interesting consequence in computable analysis: If a complete me...

Ab.llrtI(·I: Algorithm, based 011 minimIsation of fuzzy compactness are developed whereby it is possible to obtain automatically both fuzzy and nonfu77y skeletons of an image. Compactness measure lakes into account the fuzziness In geometry of regions in an image. The memberstlip plane representing the subset 'Core line' is made gray level and position dependent sueb thai its value decreases as...