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Shape theory of maps.

Zvonko Cerin (1995)

Revista Matemática de la Universidad Complutense de Madrid

We shall describe a modification of homotopy theory of maps which we call shape theory of maps. This is accomplished by constructing the shape category of maps HMb. The category HMb is built using multi-valued functions. Its objects are maps of topological spaces while its morphisms are homotopy classes of collections of pairs of multi-valued functions which we call multi-binets. Various authors have previously given other descriptions of shape categories of maps. Our description is intrinsic in...

Size levels for arcs

Sam Nadler, T. West (1992)

Fundamenta Mathematicae

We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.

Smoothness and the property of Kelley

Janusz Jerzy Charatonik, Włodzimierz J. Charatonik (2000)

Commentationes Mathematicae Universitatis Carolinae

Interrelations between smoothness of a continuum at a point, pointwise smoothness, the property of Kelley at a point and local connectedness are studied in the paper.

Currently displaying 21 – 40 of 107