On the Categories of Weak and Strong LM-G-Filter Spaces

Abstract

In this paper, the authors introduce the notion of weak r-level LM-G-filter spaces and strong p-level LM-G-filter spaces and discuss certain properties of these spaces. The study identifies [Formula: see text]-G, the category of weak r-level LM-G-filter spaces as an isomorphism-closed bireflective full subcategory of LM-G, the category of LM-G-filter spaces. It is also proved that [Formula: see text]-G, the category of strong p-level LM-G-filter spaces is an isomorphism-closed bicoreflective full subcategory of LM-G. Moreover, level decompositions of LM-G-filter spaces are studied and some properties of the associated L-pre G-filter spaces are obtained.

Keywords

• Weak r-level LM-G-filter spaces
• strong p-level LM-G-filter spaces
• initial structures
• fibre smallness
• reflective subcategory
• coreflective subcategory