On Generalized Weak Structures

Abstract

Avila and Molina [1] introduced the notion of generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures and the structures <em>α </em>(<em>g</em>),<em>π </em>(<em>g</em>),<em>σ</em> (<em>g</em>) and <em>β</em> (<em>g</em>). This work is a further investigation of generalized weak structures due to Avila and Molina. Further we introduce the structures <em>ro</em>(<em>g</em>) and <em>rc</em>(<em>g</em>) and study the properties of the structures <em>ro</em>(<em>g</em>), <em>rc</em>(<em>g</em>), and also further properties of <em>α </em>(<em>g</em>),<em>π </em>(<em>g</em>),<em>σ</em> (<em>g</em>) and <em>β</em> (<em>g</em>) due to [1].