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On the base dimension I for (compact) spacesстатья
- Авторы: Chatyrko Vitalij A., Iliadis Stavros D., Kozlov Konstantin L.
- Журнал: Questions and Answers in General Topology
- Том: 28
- Номер: 2
- Год издания: 2010
- Первая страница: 173
- Последняя страница: 185
- Аннотация: S. Iliadis introduced the notion of the so-called b^n-Ind<=\alpha-dimensional normal base F for the closed subsets of a space X, where \alpha is an ordinal, which is defined similarly to the classical large inductive dimension. In this case, here we shall write $I(X, F)<=\alpha and say that the base dimension I of X by the normal base F is less than or equal to \alpha. The classical large inductive dimension Ind of a normal space X, the large inductive dimension Ind_0 of a Tychonoff space X (due to M. Charalambous and V. Filippov) and the relative large inductive dimension defined by A. Chigogidze may be considered as a special case of the base dimension I: Ind(X)=I(X, Z(X)), Ind_0(X)= I(X,Z_0(X)) and I(X, Y)= I(X, Z(X,Y)) where Z(X) is the normal base of all closed subsets of X, Z_0(X) is the normal base of all functionally closed subsets (zero-sets) of X and Z(X,Y)=Z_0(Y)\cap X for X\subset Y. In this paper we study the behavior of the base dimension I for (compact) spaces. Sum and product theorems are presented. An answer (see Theorems 4.14 and 5.3) to [8, Question 3] about the relationship between the base dimensions I for different normal bases of a space is given.
- Добавил в систему: Козлов Константин Леонидович