On axioms of convergence in linear spaces - Kamiński, Andrzej (Annales Mathematicae Silesianae, 1985)
By a (general) convergence in a given linear space X we mean a mapping G: XN→2X, where N denotes the set of all positive integers, and by a zero-convergence in X we mean a convergence G0 in X for which G0(x)≠⌀ implies 0∈G0(x) for each x∈XN. In the paper, the two operations are defined: 1° operation C, which to each zero-convergence G0 in X assigns some general convergence G in X, and 2° operation C0, which to each general convergence G in X assigns a zero-convergence G0 in X. Various systems of axioms for general convergences and zero-convergences are considered and their connections with the operations C and C0 are studied. Also mutual independence of axioms is studied.