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Cartesian Products of Relations and Relational Structures
, 1996
"... In this paper the definitions of cartesian products of relations and relational structures are introduced. Facts about these notions are proved. This work is the continuation of formalization of [8]. ..."
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Cited by 22 (6 self)
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In this paper the definitions of cartesian products of relations and relational structures are introduced. Facts about these notions are proved. This work is the continuation of formalization of [8].
Definitions and Properties of the Join and Meet of Subsets
, 1996
"... This paper is the continuation of formalization of [4]. The definitions of meet and join of subsets of relational structures are introduced. The properties of these notions are proved. MML Identifier: YELLOW_4 ..."
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Cited by 12 (2 self)
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This paper is the continuation of formalization of [4]. The definitions of meet and join of subsets of relational structures are introduced. The properties of these notions are proved. MML Identifier: YELLOW_4
On the characterizations of compactness
 Journal of Formalized Mathematics
"... Summary. In the paper we show equivalence of the convergence of filters on a topological space and the convergence of nets in the space. We also give, five characterizations of compactness. Namely, for any topological space T we proved that following condition are equivalent: • T is compact, • every ..."
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Cited by 8 (1 self)
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Summary. In the paper we show equivalence of the convergence of filters on a topological space and the convergence of nets in the space. We also give, five characterizations of compactness. Namely, for any topological space T we proved that following condition are equivalent: • T is compact, • every ultrafilter on T is convergent, • every proper filter on T has cluster point, • every net in T has cluster point, • every net in T has convergent subnet, • every Cauchy net in T is convergent.
On ordering of bags
 Journal of Formalized Mathematics
"... Summary. We present a Mizar formalization of chapter 4.4 of [8] devoted to special orderings in additive monoids to be used for ordering terms in multivariate polynomials. We have extended the treatment to the case of infinite number of variables. It turns out that in such case admissible orderings ..."
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Cited by 6 (1 self)
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Summary. We present a Mizar formalization of chapter 4.4 of [8] devoted to special orderings in additive monoids to be used for ordering terms in multivariate polynomials. We have extended the treatment to the case of infinite number of variables. It turns out that in such case admissible orderings are not necessarily well orderings. MML Identifier:BAGORDER. WWW:http://mizar.org/JFM/Vol14/bagorder.html
Development of the theory of continuous lattices in mizar
 In Kerber and Kohlhase
, 2001
"... Abstract. This paper reports on Mizar formalization of the theory of continuous lattices included in the A Compendium of Continuous Lattices, [7]. Mizar formalization means a formalization of theorems, definitions, and proofs in the Mizar language such that it is accepted by the Mizar system. This e ..."
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Cited by 5 (3 self)
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Abstract. This paper reports on Mizar formalization of the theory of continuous lattices included in the A Compendium of Continuous Lattices, [7]. Mizar formalization means a formalization of theorems, definitions, and proofs in the Mizar language such that it is accepted by the Mizar system. This effort was originally motivated by the question whether the Mizar system is sufficiently developed as to allow expressing advanced mathematics. The current state of the formalization, which includes 49 Mizar articles written by 14 authors, suggests that the answer is positive. The work of the team of authors in cooperation with the Library Committee1 and system designers resulted in improvements of the system towards a more convenient technology for doing mechanically checked mathematics. It revealed, also, that the substantial element of the convenience is the incorporation of computer algebra into Mizar system. 1