On the connectedness of a random closed set of a Euclidean space

Autor:	Rafael M. Rubio, Jónatan Herrera, Juan J. Salamanca
Rok vydání:	2022
Předmět:	Set (abstract data type) Discrete mathematics Closed set Artificial Intelligence Logic Euclidean space Social connectedness Abstract simplicial complex Characterization (mathematics) Topology (chemistry) Mathematics
Zdroj:	Fuzzy Sets and Systems. 443:127-136
ISSN:	0165-0114
Popis:	Our aim is to obtain a suitable characterization of certain topological properties of a random closed set through its capacity functional. The main technique mixes two different fields: on the one hand, the abstract simplicial complex associated to a covering, whose topology coincides with the topology of the original set thanks to the nerve theorem. On the other hand, the celebrated Choquet-Kendall-Matheron theorem, which states that a random closed set is characterized by its capacity functional.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::0472b76c9d67edd7cad4259a3066370b https://doi.org/10.1016/j.fss.2021.09.024 Zobrazit plný text záznamu Full Text from ScienceDirect