On categories of merotopic, nearness, and filter algebras

Subject Areas : History and biography

V.  Gompa ¹ (Department Head and Professor of Mathematics, Jacksonville State University, Jacksonville, AL 36265, USA)

Received: 2016-05-02 Accepted : 2016-06-10 Published : 2016-08-01

Keywords: topological algebra, Universal algebra, nearness spaces, merotopic spaces, filter spaces,

Abstract :

We study algebraic properties of categories of Merotopic, Nearness, and Filter Algebras. We show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. The forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the category of filters has a left adjoint.

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