Projective system of topological quasi modules
Subject Areas : General topology
S. Jana
1
(Department of Pure Mathematics, Calcutta University, 35-Ballygaunge Circular Road, Kolkata-700019, India)
S. Mazumder
2
(Department of Mathematics, Adamas University, Barasat-Barrackpore Road, Jagannathpur, Kolkata, India)
Keywords: Quasi module, topological quasi module, projective system, projective limit,
Abstract :
Quasi module is a new algebraic structure, based on module, which is composed of a semigroup structure and a partial order accompanied with an external ring multiplication. We proposed this structure in our paper \cite{qmod} while we were studying the hyperspace $ \com{M}{} $ consisting of all nonempty compact subsets of a topological module $ M $ over some topological ring $ R $. Quasi module can be considered as a generalisation of module in some sense. In the present paper we have defined topological quasi module and given some examples of it. We have shown that the Cartesian product of arbitrary family of topological quasi modules is again a topological quasi module over some topological unitary ring. Finally we have defined projective system of topological quasi modules and projective limit of this system. We have proved various topological properties of the projective limit of a projective system.
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