*-Topological properties
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:...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1990-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171290000734 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849304655296724992 |
|---|---|
| author | T. R. Hamlett David Rose |
| author_facet | T. R. Hamlett David Rose |
| author_sort | T. R. Hamlett |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-41af18cd8e4b4b0c8bf4e147a621206b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1990-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-41af18cd8e4b4b0c8bf4e147a621206b2025-08-20T03:55:40ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251990-01-0113350751210.1155/S0161171290000734*-Topological propertiesT. R. Hamlett0David Rose1Department of Mathematics, East Central University, Ada 74820, Oklahoma, USADepartment of Mathematics, East Central University, Ada 74820, Oklahoma, USAAn 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.http://dx.doi.org/10.1155/S0161171290000734idealregular opensemi-opensemi-homeomorphismsemi-topological propertysemiregularcompatible idealtopological property*-topological propertyτ-boundary idealnowhere dense setsmeager sets. |
| spellingShingle | T. R. Hamlett David Rose *-Topological properties International Journal of Mathematics and Mathematical Sciences ideal regular open semi-open semi-homeomorphism semi-topological property semiregular compatible ideal topological property *-topological property τ-boundary ideal nowhere dense sets meager sets. |
| title | *-Topological properties |
| title_full | *-Topological properties |
| title_fullStr | *-Topological properties |
| title_full_unstemmed | *-Topological properties |
| title_short | *-Topological properties |
| title_sort | topological properties |
| topic | ideal regular open semi-open semi-homeomorphism semi-topological property semiregular compatible ideal topological property *-topological property τ-boundary ideal nowhere dense sets meager sets. |
| url | http://dx.doi.org/10.1155/S0161171290000734 |
| work_keys_str_mv | AT trhamlett topologicalproperties AT davidrose topologicalproperties |