Martin Sleziak

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We prove that every topological space (T0-space, T1-space) can be embedded in a pseudoradial space (in a pseudoradial T0-space, T1-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.
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)
This thesis deals mainly with hereditary coreflective subcategories of the category Top of topological spaces. After preparing the basic tools used in the rest of thesis we start by a question which coreflective subcategories of Top have the property SA = Top (i.e., every topological space can be embedded in a space from A). We characterize such classes by(More)
The first known examples of subsequential countably compact Hausdorff (T2) spaces that are not sequential are given here, including one that is Tychonoff under CH. The sequential extensions of such spaces cannot be T2, but the extensions we construct are T1. The problem of whether it is consistent for there to be a compact T2 subsequential, non-sequential(More)
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. 1 Generalizations of limit The notion of limit is one of the central notions in mathematical(More)
In this talk I would like to speak about density measures and Lévy group. Density measures are extensions of asymptotic density to the whole power set P(N). Lévy group G is a certain group of permutations of N. (Precise definitions will follow immediately.) Both the Lévy group and the density measures have found applications in number theory and, more(More)
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