Glasnik Matematicki, Vol. 36, No.2 (2001), 247-262.


Takahisa Miyata

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, X1, X0 X1 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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