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Introduction to Go-Board - Part II
, 2002
"... this paper. 1. REAL NUMBERS PRELIMINARIES For simplicity, we use the following convention: f , f 1 , f 2 , g denote finite sequences of elements of E T , v, v 1 , v 2 denote finite sequences of elements of R, n, m, i, j, k denote natural numbers, and G denotes a Go-board ..."
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Cited by 19 (4 self)
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this paper. 1. REAL NUMBERS PRELIMINARIES For simplicity, we use the following convention: f , f 1 , f 2 , g denote finite sequences of elements of E T , v, v 1 , v 2 denote finite sequences of elements of R, n, m, i, j, k denote natural numbers, and G denotes a Go-board
Projections in n-Dimensional Euclidean Space to Each Coordinates
, 1997
"... this paper. 1. PROJECTIONS For simplicity, we use the following convention: s 1 , r, r 1 , r 2 denote real numbers, s denotes a real number, n, i denote natural numbers, X denotes a non empty topological space, p, p 1 , p 2 denote points of E T , and P denotes a subset of E T . Let n, i be natur ..."
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Cited by 2 (2 self)
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this paper. 1. PROJECTIONS For simplicity, we use the following convention: s 1 , r, r 1 , r 2 denote real numbers, s denotes a real number, n, i denote natural numbers, X denotes a non empty topological space, p, p 1 , p 2 denote points of E T , and P denotes a subset of E T . Let n, i be natural numbers and let p be an element of the carrier of E T . The functor Proj(p, i) yielding a real number is defined as follows: (Def. 1) For every finite sequence g of elements of R such that g = p holds Proj(p, i) = g i
Go-Board Theorem
, 1999
"... this paper. For simplicity, we adopt the following convention: p, p 1 , p 2 , q 1 , q 2 denote points of E ..."
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Cited by 2 (0 self)
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this paper. For simplicity, we adopt the following convention: p, p 1 , p 2 , q 1 , q 2 denote points of E
Bounded Domains and Unbounded Domains
, 2003
"... this paper. 1. DEFINITIONS OF BOUNDED DOMAIN AND UNBOUNDED DOMAIN We follow the rules: m, n are natural numbers, r, s are real numbers, and x, y are sets. We now state several propositions: (1) If r 0, then |r| =-r ..."
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this paper. 1. DEFINITIONS OF BOUNDED DOMAIN AND UNBOUNDED DOMAIN We follow the rules: m, n are natural numbers, r, s are real numbers, and x, y are sets. We now state several propositions: (1) If r 0, then |r| =-r
Bounding Boxes for Compact Sets in Ε²
, 1997
"... this paper. 1. Preliminaries Let X be a set. Let us observe that X has non empty elements if and only if: (Def. 1) 0 / # X. We introduce X is without zero as a synonym of X has non empty elements. We introduce X has zero as an antonym of X has non empty elements. Let us note that R has zero and ..."
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this paper. 1. Preliminaries Let X be a set. Let us observe that X has non empty elements if and only if: (Def. 1) 0 / # X. We introduce X is without zero as a synonym of X has non empty elements. We introduce X has zero as an antonym of X has non empty elements. Let us note that R has zero and N has zero. Let us note that there exists a set which is non empty and without zero and there exists a set which is non empty and has zero. Let us observe that there exists a subset of R which is non empty and without zero and there exists a subset of R which is non empty and has zero. The following proposition is true (1) For every set F such that F is non empty and #-linear and has non empty elements holds F is centered. Let
