In this book the authors for the first time introduce a new type of topological spaces called the set ideal topological spaces using rings or semigroups, or used in the mutually exclusive sense. This type of topological spaces use the class of set ideals of a ring (semigroups). The rings or semigroups can be finite or infinite order. By this method we get complex modulo finite integer set ideal topological spaces using finite complex modulo integer rings or finite complex modulo integer semigroups. Also authors construct neutrosophic set ideal toplogical spaces of both finite and infinite order as well as complex neutrosophic set ideal topological spaces. Several interesting properties about them are defined, developed and discussed in this book. The authors leave it as an open conjecture whether the number of finite topological spaces built using finite sets is increased by building these classes of set ideal topological spaces using finite rings or finite semigroups.
Zip Publishing, Ohio
set ideal topological spaces, rings, semigroups
Smarandache, Florentin and W.B. Vasantha Kandasamy. "Set Ideal Topological Spaces." (2012). https://digitalrepository.unm.edu/math_fsp/261
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