Closed hereditary additive and divisible subcategories in epireflective subcategories of top
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Abstract
The aim of this paper is to investigate closed hereditary additive and divisible (AD) subcategories of epireflective subcategories of the category Top. In quotient reflective subcategories of Top AD subcategories are precisely the coreflective subcategories. We describe the closed hereditary AD hull and the closed hereditary AD kernel of AD subcategories and present some results concerning minimal non-trivial closed hereditary AD subcategories in epire ective subcategories of Top. We also show that some of the results obtained for AD subcategories are not valid in the case of coreflective subcategories in epireflective subcategories that arenot quotient reflective, for instance in the category of Tychonoff spaces.
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Lackova, V.
(2014).
Closed hereditary additive and divisible subcategories in epireflective subcategories of top.
Acta Mathematica Universitatis Comenianae, 83(1), 135-146.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/4/13
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References
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2. Arkhangel'skii A. V. and Ponomarev V. I., Fundamentals of General Topology: Problems and Exercises, D. Reidel Publishing Company, Dordrecht (1983).
3. Cincura J., Heredity and core ective subcategories of the category of topological spaces, Appl. Categ. Structures 9 (2001), 131-138.
4. Cincura J., Hereditary core ective subcategories of categories of topological spaces, Appl. Categ. Structures 13 (2005), 329-342.
5. Cincura J., Hereditary core ective subcategories of the categories of Tychono and zero-dimensional spaces, Appl. Categ. Structures, to appear.
6. Engelking R., General topology, revised and completed edition, Heldermann Verlag, Berlin (1989).
7. Herrlich H., Topologische Reflexionen und Coreflexionen, Springer, Berlin (1968).
8. Herrlich H. and Husek M., Some open categorical problems in Top, Appl. Categ. Structures 1 (1993), 1-19.
9. Kannan V., Coreflexive subcategories in topology, PhD thesis, Madurai University (1970).
10. Kannan V., Reflexive cum Coreflexive Subcategories in Topology, Math. Ann. 195 (1972), 168-174.
11. Ordinal invariants in topology, Mem. Amer. Math. Soc. 245 (1981).
12. Lukacs G., A convenient subcategory of Tych, Appl. Categ. Structures 12 (2004), 369-377.
13. Noble N., Countably compact and pseudocompact products, Czechoslovak Mathematical Journal 19 (1969), 390-397.
14. Noble N., The continuity of functions on cartesian products, Trans. Amer. Math. Soc. 149 (1970), 187-198.
15. Sleziak M., On hereditary core ective subcategories of Top, Appl. Categ. Structures 12 (2004), 301-317.
16. Sleziak M., Hereditary, additive and divisible classes in epireflective subcategories of Top, Appl. Categ. Structures 16 (2008), 451-478.