Glasnik Matematicki, Vol. 36, No.2 (2001), 247-262.
n-SHAPE EQUIVALENCE AND TRIADS
Department of Computer Science, Shizuoka Institute of Science and
Technology, 2200-2 Toyosawa, Fukuroi, 437-8555 Japan
Division of Mathematics and Informatics, Faculty of Human
Development, Kobe University, 3-11 Tsurukabuto, Nada-Ku,
Kobe, 657-8501 Japan
Abstract. This paper concerns the shape theory for
triads of spaces which was intoduced by the author. More precisely,
in the forst part, the shape dimension for triads of spaces
(X; X0, X1) is
introduced, and its upper and lower bounds are given in terms
of the shape dimension of X0,
and X. In the second part, a Whitehead type theorem for
triad of spaces and a Mayer-Vietoris type theorem concerning
n-shape equivalence are obtained.
1991 Mathematics Subject Classification.
54C56, 55P55, 55Q07.
Key words and phrases. Shape, triad, n-shape
equivalence, Whitehead theorem, shape dimension.
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