Idealization of Ganster-Reilly decomposition theorems
Abstract
In 1990, Ganster and Reilly proved that a function is continuous if and only if it is precontinuous and LC-continuous. In this paper we extend their decomposition of continuity in terms of ideals. We show that a function f (X,τ, I) (Y,σ) is continuous if and only if it is pre-I-continuous and I-LC-continuous. We also provide a decomposition of I-continuity.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.