Convergence of relations in convergence spaces
Convergence of relations in convergence spaces
The author studies convergences on power sets and on families of relations. The paper examines the known convergence structures: adhering convergence, compact convergence, semiconvergence, and persistence convergence. Related convergences n the appropriate spaces of relations are defined via the structure of continuous convergence. Preservation of these structure types under compositions are investigated. For a type of convergence structure on hyperspaces not listed in the references of this paper, see \textit{R. J. Gazik} [Proc. Am. Math. Soc. 37, 81-89 (1973; Zbl 0231.54004)].
Function spaces in general topology, compact convergence, filtered families, persistence convergence, semiconvergence, compositions, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), Hyperspaces in general topology, continuous convergence, adhering convergence
Function spaces in general topology, compact convergence, filtered families, persistence convergence, semiconvergence, compositions, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), Hyperspaces in general topology, continuous convergence, adhering convergence
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