Arenas et al. [1] introduced the notion of lambda-closed sets as a generalization of locally closed sets. In this paper, we introduce the notions of lambda-locally closed sets, Lambda_lambda-closed sets and lambda_g-closed sets and obtain some decompositions of closed sets and continuity in topological spaces.

by Logan M. Axon Algorithmic randomness in the Cantor space, 2 ω , has recently become the subject of intense study. Originally defined in terms of the fair coin measure, algorithmic randomness has since been extended, for example in Reimann and Slaman [22, 23], to more general measures. Others have meanwhile developed definitions of algorithmic randomness for different spaces, for example the ...

State estimation entails the estimation of an unobserved random closed set from (partial) observation of an associated random set. Examples include edge effect correction, cluster detection, filtering and prediction. We focus on inference for random sets based on points sampled on its boundary. Such data are subject to mis-alignment and noise. First, we ignore mis-alignment and discuss maximum ...

the main purpose of this paper is to introduce and study new classes of soft closed sets like soft regular generalized b-closed sets in soft topological spaces (brie y soft rgb-closed set) moreover, soft rg-closed, soft gpr-closed, soft gb-closed, soft gsp-closed, soft g-closed, soft gb-closed, and soft sgb-closed sets in soft topological spaces are introduced in this paper and we investigat...

Martin-Löf randomness was originally defined and studied in the context of the Cantor space 2ω . In [1] probability theoretic random closed sets (RACS) are used as the foundation for the study of Martin-Löf randomness in spaces of closed sets. Here we focus on the space of closed subsets of R and a particular family of measures on this space, the generalized Poisson processes. This gives a nove...

In this article, we study several aspects of the intersections algorithmically random closed sets. First, answer a question Cenzer and Weber, showing that operation intersecting relatively sets (random with respect to certain underlying measures induced by Bernoulli on space codes sets), which preserves randomness, can be inverted: set appropriate type obtained as intersection two We then exten...

We theoretically formulate the problem of processing continuous-space binary random fields by means of mathematical morphology. This may allow us to employ mathematical morphology to develop new statistical techniques for the analysis of binary random images. Since morphological transformations of continuous-space binary random fields are not measurable in general, we are naturally forced to em...