文章基本信息

标题：<mml:math alttext="$*$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>*</mml:mo></mml:math>-Topological properties
本地全文：下载
作者：T. R. Hamlett ; David Rose
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1990
卷号：13
DOI：10.1155/S0161171290000734
出版社：Hindawi Publishing Corporation
摘要：An ideal on a set X is a nonempty collection of subsets of X closed under the operations of subset (heredity) and finite unions (additivity). Given a topological space (X,τ) an ideal ℐ on X and A⊆X, ψ(A) is defined as ⋃{U∈τ:U−A∈ℐ}. A topology, denoted τ*, finer than τ is generated by the basis {U−I:U∈τ,I∈ℐ}, and a topology, denoted 〈ψ(τ)〉, coarser than τ is generated by the basis ψ(τ)={ψ(U):U∈τ}. The notation (X,τ,ϑ) denotes a topological space (X,τ) with an ideal ℐ on X. A bijection f:(X,τ,ℐ)→(Y,σ,J) is called a *-homeomorphism if f:(X,τ*)→(Y,σ*) is a homeomorphism, and is called a ψ-homeomorphism if f:(X,〈ψ(τ)〉)→(Y,〈ψ(σ)〉) is a homeomorphism. Properties preserved by *-homeomorphisms are studied as well as necessary and sufficient conditions for a ψ -homeomorphism to be a *-homeomorphism. The semi-homeomorphisms and semi-topological properties of Crossley and Hildebrand [Fund. Math., LXXIV (1972), 233-254] are shown to be special case.