Abstract

In ideal topological spaces, $\star$-dense in itself subsets are used to characterize ideals and mappings. In this note, properties of ${\cal A}_{\cal I}$-sets, ${\cal I}$-locally closed sets and almost strong ${\cal I}$-open sets are discussed. We characterize codense ideals by the collection of these sets. Also, we give a decomposition of continuous mappings and deduce some well-known results.

Keywords: Codense ideal, semiopen set, preopen set, ${\cal I}$-locally closed set, $f_{\cal I}$-set, regular ${\cal I}$-closed set, ${\cal A}_{\cal I}$-set, semicontinuity, ${\cal A}_{\cal I}$-continuity, $f_{\cal I}$-continuity.

MSC: 54A05, 54A10, 54C08, 54C10

Pages:  75$-$84     

Volume  59 ,  Issue  3 ,  2007