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76
Basis of Real Linear Space
, 1990
"... this paper. For simplicity, we follow the rules: x is a set, a, b are real numbers, V is a real linear space, W 1 , W 2 , W 3 are subspaces of V , v, v 1 , v 2 are vectors of V , A, B are subsets of the carrier of V , L, L 1 , L 2 are linear combinations of V , l is a linear combination of A, F , G ..."
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Cited by 250 (21 self)
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this paper. For simplicity, we follow the rules: x is a set, a, b are real numbers, V is a real linear space, W 1 , W 2 , W 3 are subspaces of V , v, v 1 , v 2 are vectors of V , A, B are subsets of the carrier of V , L, L 1 , L 2 are linear combinations of V , l is a linear combination of A, F , G
Directed sets, nets, ideals, filters, and maps
 Journal of Formalized Mathematics
, 1996
"... Summary. Notation and facts necessary to start with the formalization of continuous lattices according to [8] are introduced. The article contains among other things, the definition of directed and filtered subsets of a poset (see 1.1 in [8, p. 2]), the definition of nets on the poset (see 1.2 in [8 ..."
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Cited by 111 (30 self)
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Summary. Notation and facts necessary to start with the formalization of continuous lattices according to [8] are introduced. The article contains among other things, the definition of directed and filtered subsets of a poset (see 1.1 in [8, p. 2]), the definition of nets on the poset (see 1.2 in [8, p. 2]), the definition of ideals and filters and the definition of maps preserving arbitrary and directed sups and arbitrary and filtered infs (1.9 also in [8, p. 4]). The concepts of semilattices, supsemiletices and poset lattices (1.8 in [8, p. 4]) are also introduced. A number of facts concerning the above notion and including remarks 1.4, 1.5, and 1.10 from [8, pp. 3–5] is presented.
Combining of Circuits
, 2002
"... this paper. 1. COMBINING OF MANY SORTED SIGNATURES Let S be a many sorted signature. A gate of S is an element of the operation symbols of S ..."
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Cited by 90 (24 self)
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this paper. 1. COMBINING OF MANY SORTED SIGNATURES Let S be a many sorted signature. A gate of S is an element of the operation symbols of S
An Overview of the MIZAR Project
 UNIVERSITY OF TECHNOLOGY, BASTAD
, 1992
"... The Mizar project is a longterm effort aimed at developing software to support a working mathematician in preparing papers. A. Trybulec, the leader of the project, has designed a language for writing formal mathematics. The logical structure of the language is based on a natural deduction system ..."
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Cited by 82 (1 self)
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The Mizar project is a longterm effort aimed at developing software to support a working mathematician in preparing papers. A. Trybulec, the leader of the project, has designed a language for writing formal mathematics. The logical structure of the language is based on a natural deduction system developed by Ja'skowski. The texts written in the language are called Mizar articles and are organized into a data base. The TarskiGrothendieck set theory forms the basis of doing mathematics in Mizar. The implemented processor of the language checks the articles for logical consistency and correctness of references to other articles.
Families of Subsets, Subspaces and Mappings in Topological Spaces
"... This article is a continuation of [13]. Some basic theorems about families of sets in a topological space have been proved. Following redefinitions have been made: singleton of a set as a family in the topological space and results of boolean operations on families as a family of the topological spa ..."
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Cited by 63 (0 self)
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This article is a continuation of [13]. Some basic theorems about families of sets in a topological space have been proved. Following redefinitions have been made: singleton of a set as a family in the topological space and results of boolean operations on families as a family of the topological space. Notion of a family of complements of sets and a closed (open) family have been also introduced. Next some theorems refer to subspaces in a topological space: some facts about types in a subspace, theorems about open and closed sets and families in a subspace. A notion of restriction of a family has been also introduced and basic properties of this notion have been proved. The last part of the article is about mappings. There are proved necessary and sufficient conditions for a mapping to be continuous. A notion of homeomorphism has been defined next. Theorems about homeomorphisms of topological spaces have been also proved. MML Identifier: TOPS2.
On the Decomposition of the States of SCM
, 1993
"... This article continues the development of the basic terminology ..."
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Cited by 52 (1 self)
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This article continues the development of the basic terminology
On Defining Functions on Trees
, 2003
"... this paper. 1. PRELIMINARIES One can prove the following propositions: (1) For every non empty set D holds every finite sequence of elements of FinTrees(D) is a finite sequence of elements of Trees(D) ..."
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Cited by 50 (22 self)
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this paper. 1. PRELIMINARIES One can prove the following propositions: (1) For every non empty set D holds every finite sequence of elements of FinTrees(D) is a finite sequence of elements of Trees(D)
Function Domains and Fraenkel Operator
, 1990
"... this paper. In this paper A, B are non empty sets and X is a set. In this article we present several logical schemes. The scheme Fraenkel5' concerns a non empty set A; a unary functor F yielding a set, and two unary predicates P ; Q; and states that: ..."
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Cited by 22 (6 self)
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this paper. In this paper A, B are non empty sets and X is a set. In this article we present several logical schemes. The scheme Fraenkel5' concerns a non empty set A; a unary functor F yielding a set, and two unary predicates P ; Q; and states that: