The -super socle of the ring of continuous functions

• Main Authors: Simin Mehran, Mehrdad Namdari
• Format: Article
• Language: English
• Published: Shahid Beheshti University 2017-01-01
• Series: Categories and General Algebraic Structures with Applications
• Subjects: -isolated point; one-point -compactication; lambda-supre socle; lambda-isolated point; one-point lambda-compactifcation; P_lambda-space
• Online Access: http://www.cgasa.ir/article_33814.html
• ISSN: 2345-5853; 2345-5861

The concept of λ-super socle of C(X), denoted by Sλ(X) (i.e., the set of elements of C(X) such that the cardinality of their cozerosets are less than λ, where λ is a regular cardinal number with λ≤|X|) is introduced and studied. Using this concept we extend some of the basic results concerning SCF(X), the super socle of C(X) to Sλ(X), where λ≥ℵ0. In particular, we determine spaces X for which SCF(X) and Sλ(X) coincide. The one-point λ-compactification of a discrete space is algebraically characterized via the concept of λ-super socle. In fact we show that X is the one-point λ-compactification of a discrete space Y if and only if Sλ(X) is a regular ideal and Sλ(X)=Ox, for some x∈X. .