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The main goal of this paper is to introduce the notion of stabilizers in L-algebras and develop stabilizer theory in L-algebras. In this paper, we introduced the notions of left and right stabilizers and investigated some related properties of them. Then, we discussed the relations among stabilizers, ideal and co-annihilators. Also, we obtained that the set of all ideals of a CKL-algebra forms a relative pseudo-complemented lattice. In addition, we proved that right stabilizers in CKL-algebra are ideals. Then by using the right stabilizers we produced a basis for a topology on L-algebra. We showed that the generated topology by this basis is Baire, connected, locally connected and separable and we investigated the other properties of this topology. [ABSTRACT FROM AUTHOR]

In this paper, the notions of (para, quasi, semi) topological MV-algebras are defined and their related properties are studied. Also, topologies with which an MV-algebra can be a (para, semi) topological MV-algebra are obtained. Clearly, a topological MV-algebra is a (para, quasi, semi) topological MV-algebra, but the converse is not true, as shown by an example. In addition, we study ideals and filters in (para, quasi) topological MV-algebras, and we show that a quasitopological MV-algebra is a topological MV-algebra if the ideal {0}, or equivalently, the filter {1} is open. [ABSTRACT FROM AUTHOR]