p. 135 - 146 Closed hereditary additive and divisible subcategories in epireflective subcategories of Top V. Lacková Received: June 24, 2013; Accepted: December 9, 2013 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 epireflective 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 are not quotient reflective, for instance, in the category of Tychonoff spaces. Keywords: epireflective subcategory; coreflective subcategory; additive and divisible subcategory; closed hereditary subcategory. AMS Subject classification: Primary: 18D15, 54B30 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2014, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |