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

n-SHAPE EQUIVALENCE AND TRIADS

Takahisa Miyata

Division of Mathematics and Informatics, Faculty of Human Development, Kobe University, 3-11 Tsurukabuto, Nada-Ku, Kobe, 657-8501 Japan
e-mail: tmiyata@kobe-u.ac.jp

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.