Small inductive dimension and Alexandroff 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...
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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 ...
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This article is concerned with Alexandroff L-topological spaces and L-co-topological spaces, where L is a commutative, unital quantale. On one hand, an example is given to show that there is a finite strong L-topological space that is not Alexandroff. On the other hand, it is proved that every finite strong L-co-topological space is Alexandroff and that the category of Alexandroff strong L-co-t...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2014
ISSN: 0166-8641
DOI: 10.1016/j.topol.2014.02.014