Home / Volume 1 - 2021 /
IDEALIZATION OF A DECOMPOSITION THEOREM
Article Name
IDEALIZATION OF A DECOMPOSITION THEOREM
Volume & Issue
Volume 1 - 2021 / Issue 1 - August
Authors
M.Sebasti Jeya Pushpam
Keywords
α-continuous and A-continuous, α-I-continuous and AI -continuous
Abstract
In 1986, Tong [13] proved that a function f :(X, τ ) → (Y,φ ) is continuous if and only if it is α-continuous and A-continuous. We extend this decomposition of continuity in terms of ideals. First, we introduce the notions of regular-I-closed sets, AI -sets and AI -continuous functions in ideal topological spaces and investigate their properties. Then, we show that a function f :(X, τ , I)→ (Y,φ ) is continuous if and only if it is α-I-continuous and AI -continuous