Document Type: Research Paper

Author

Department Head and Professor of Mathematics, Jacksonville State University, Jacksonville, AL 36265, USA

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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Main Subjects

[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and Concrete Categories. John Wiley & Sons, Inc., New York, 1990.

[2] P. M. Cohn, Universal Algebra. Harper and Row, Publishers, New York, 1965.

[3] V. L. Gompa, Essentially algebraic functors and topological algebra. Indian Journal of Mathematics, 35, (1993), 189-195.

[4] H. Herrlich, A concept of nearness. General Topology and its Applications 4 (1974), 191-212.

[5] H. Herrlich, Topological structures. In: Topological structures. Math. Centre Tracts 52 (1974), 59-122.

[6] H. Herrlich, G. E. Strecker, Category Theory. Allyn and Bacon, Boston, 1973.

[7] Y. H. Hong, Studies on categories of universal topological algebras. Doctoral Dissertation, McMaster University, 1974.

[8] M. Katetov, On continuity structures and spaces of mappings. Comment. Math. Univ. Carol. 6 (1965), 257 - 278.

[9] M. Katetov, Convergence structures. General Topology and its Applications II, Academic Press, New York (1967), 207-216.

[10] O. Wyler, On the categories of general topology and topological algebras. Arc. Math. (Basel) 22 (1971), 7-17.