ABOUT BASES AND PRE-BASES OF MAPPINGS
Keywords:
topological space, mapping base, prebase of a mapping, weight of a mapping, countability axioms, cardinal numberAbstract
This article examines set-theoretic and topological characteristics of continuous mappings, extending the classical concepts of bases and networks of spaces to the case of mappings. The author introduces definitions of prenets and prebases of a mapping, proves criteria for their existence, and explores cardinal invariants such as the character and weight of a mapping. It is established that the first and second countability axioms for mappings are hereditary properties, and an analogue of the Alexandrov-Urysohn theorem on the cardinality of a base is proved.
References
1. Б. А. Пасынков. О распространении на отображения некоторых понятий и утверждений, касающихся пространств. Отображения и функторы. Сборник. Москва, Изд-во МГУ, 1984.
2. П. С. Александров, Б. А. Пасынков. Введение в теорию размерности. Изд. «Наука», Москва, 1973.
