B. Venkateswarlu, R. Vasu Babu, Getnet Alemu
Department of Mathematics
GIT, GITAM University
Visakhapatnam, 530 045, A.P., INDIA
Department of Mathematics
Shri Vishnu Engineering college for Women
Bhimavaram, 534201, W.G. Dist., A.P., INDIA
Department of Mathematics
Gondar University
Gondar, ETHIOPIA

Abstract. We discuss an equivalence of the concepts of complete lattices, Moore classes, and a one-to-one correspondence between Moore classes of subsets of a set and closure operators on . Also, we establish a correspondence between closure operators on sets and complete lattices. We describe morphisms among partially ordered sets, lattices, Moore classes, closure operators and complete lattices and discuss certain inter-relationships between these objects.

Received: September 26, 2013

AMS Subject Classification: 06A15, 06F30, 54H12

Key Words and Phrases: closure operator, Moore class, compact element, complete lattice, algebraic Lattice, frame, morphisms

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