Small Inductive Dimension of Topological Spaces
نویسندگان
چکیده
منابع مشابه
Small Inductive Dimension of Topological Spaces
For simplicity, we adopt the following rules: T , T1, T2 denote topological spaces, A, B denote subsets of T , F denotes a subset of T A, G, G1, G2 denote families of subsets of T , U , W denote open subsets of T A, p denotes a point of T A, n denotes a natural number, and I denotes an integer. One can prove the following propositions: (1) Fr(B ∩A) ⊆ FrB ∩A. (2) T is a T4 space if and only if f...
متن کاملSmall Inductive Dimension of Topological Spaces. Part II
In this paper n denotes a natural number, X denotes a set, and F1, G1 denote families of subsets of X. Let us consider X, F1. We say that F1 is finite-order if and only if: (Def. 1) There exists n such that for every G1 such that G1 ⊆ F1 and n ∈ CardG1 holds ⋂ G1 is empty. Let us consider X. Observe that there exists a family of subsets of X which is finite-order and every family of subsets of ...
متن کاملAN INDUCTIVE FUZZY DIMENSION
Using a system of axioms among with a modified definition of boundary on the basis of the intuitionistic fuzzy sets, we formulate an inductive structure for the dimension of fuzzy spaces which has been defined by Coker. This new definition of boundary allows to characterize an intuitionistic fuzzy clopen set as a set with zero boundary. Also, some critical properties and applications are establ...
متن کاملOn ( transfinite ) small inductive dimension of products ∗
In this paper we study the behavior of the (transfinite) small inductive dimension (trind) ind on finite products of topological spaces. In particular we essentially improve Toulmin’s estimation [T] of trind for Cartesian products.
متن کاملDimension theory and fuzzy topological spaces
J.M. Aarts introduced and studied a new dimension function, Hind, in 1975 and obtained several results on this function. In this paper, a new local inductive dimension function called local huge inductive dimension function denoted by locHind is introduced and studied. Furthermore, an effort is made to introduce and study dimension functions for fuzzy topological spaces. It has been possible to...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2009
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-009-0025-7