We introduce certain ideals of real-valued functions as a natural generalization of filters. We show that these ideals establish a canonical framework for the quantification of topological concepts, such as closedness, adherence, and compactness, in the setting of approach spaces. 2000 Mathematics Subject Classification. 54A05, 54D30.

In concurrency theory, there are several examples where the interleaved model of concurrency can distinguish between execution sequences which are not signiicantly diierent. One such example is sequences that diier from each other by stuttering, i. e., the number of times a state can adjacently repeat. Another example is executions that diier only by the ordering of independently executed event...

Abstract In this paper, we establish a connection between categorical closedness and nontopologizability of semigroups. particular, for the class

In concurrency theory, there are several examples where the interleaved model of concurrency can distinguish between execution sequences which are not significantly different. One such example is sequences that differ from each other by stuttering, i. e., the number of times a state can adjacently repeat. Another example is executions that differ only by the ordering of independently executed e...

Obtaining a weaker condition that preserves some inspired topological properties is always desirable. As result, we introduce the concept of infra-fuzzy topology, which subset family degrades fuzzy topology by omitting closedness under arbitrary unions. Fundamental spaces are investigated, including open and closed sets, interior closure operators, boundary set. It not possible to expect latter...