Commun. Korean Math. Soc. 2008 Vol. 23, No. 2, 169-178 Printed June 1, 2008
Sun Shin Ahn and Seok Hwan Kwon Dongguk University
Abstract : In this paper, we show how to associate certain topologies with special ideals of $BCC$-algebras on these $BCC$-algebras. We show that it is natural for $BCC$-algebras to be topological $BCC$-algebras with respect to theses topologies. Furthermore, we show how certain standard properties may arise. In addition we demonstrate that it is natural for these topologies to have many clopen sets and thus to be highly connected via the ideal theory of $BCC$-algebras.