Moore Systems and Moore Convergence Classes of Families of Nets

摘要: This paper presents a new cryptomorphic mathematical structure of the Moore system, called convergence class families nets. It is proved that, for given set $$X$$ , appropriate order relation $$\le $$ can be defined on $${\mathbb {MCCFN}}(X)$$ (the all classes nets ) and one-to-one correspondence $$\tau :({\mathbb {MCCFN}}(X),\le )\longrightarrow ({\mathbb {MS}}(X),\supseteq )$$ systems such that $$({\mathbb complete lattice isomorphism. means are structures. also (by considering restrictions pre-cotopologies pre-convergence structures cotopologies (a classical result). naturally gives approach to system pre-cotopology.