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Martin Sleziak HAD-classes in epireflective subcategories of Top Introduction Heredity of AD-classes References Basic definitions Hereditary coreflective subcategories of Top A generalization – epireflective subcategories AD-classes and HAD-classes Subcategories of Top All subcategories are assumed to be full and isomorphism-closed. subcategory of Top =… (More)

Let A be a topological space which is not finitely generated and CH(A) denote the coreflective hull of A in Top. We construct a generator of the coreflective subcategory SCH(A) consisting of all subspaces of spaces from CH(A) which is a prime space and has the same cardinality as A. We also show that if A and B are coreflective subcategories of Top such… (More)

- Martin Sleziak
- 2005

We prove that every topological space (T 0-space, T 1-space) can be embedded in a pseudoradial space (in a pseudoradial T 0-space, T 1-space). This answers the Problem 3 in [2]. We describe the smallest coreflective subcategory A of Top such that the hereditary coreflective hull of A is the whole category Top. 1 Preliminaries I'd like to present some… (More)

- Martin Sleziak
- 2006

Dedičnost', dedičné koreflektívne obaly a d'alšie vlastnosti koreflektívnych podkategorií kategorií topologick´ych priestorov Dizertačná práca RNDr. Martin SleziakŠkolitel Acknowledgments I am very grateful to my supervisor Doc. RNDr. JurajČinčura, CSc., for introducing me to the topic of this thesis and for his endless patience while he was carefully… (More)

- Martin Sleziak
- 2005

This talk is mainly concerned with two generalizations of convergence of sequences called I-convergence and I *-convergence. We will mention some other generalizations of limit which are related to I-convergence, e.g Banach limit and statistical convergence. The notion of limit is one of the central notions in mathematical analysis. No wonder it was… (More)

The first known examples of subsequential countably compact Hausdorff (T 2) spaces that are not sequential are given here, including one that is Tychonoff under CH. The sequential extensions of such spaces cannot be T 2 , but the extensions we construct are T 1. The problem of whether it is consistent for there to be a compact T 2 subsequential,… (More)

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