The Baire Property for the Space of Mappings of the First Functional Lebesgue Class

Key Points

• The study aims to analyze the Baire property of mappings from the first functional Lebesgue class, focusing on compact spaces.
• Investigated mappings of the first functional Lebesgue class, denoted as K1(X,M).
• Examined equivalence of Baire property for K1(X,{0,1}) and K1(X,M).
• Included properties of π-monolithic compact spaces.
• Identified necessary and sufficient conditions for Baire property in K1(X,G) for compact topological groups.
• Demonstrated that K1(X,{0,1}) and K1(X,M) share the same Baire property across certain compact spaces.
• Provided conditions under which K1(X,G) is Baire for any compact topological group G.
• Established that the class of π-monolithic compacta is included within the studied class.