Glasnik Matematicki, Vol. 52, No. 2 (2017), 331-350.

INTRINSIC STRONG SHAPE FOR PARACOMPACTA

Beti Andonovic and Nikita Shekutkovski

Faculty of Mathematics and Natural Sciences, Ss Cyril and Methodius University , 1000 Skopje, Macedonia
e-mail: nikita@pmf.ukim.mk

Abstract.   In this paper an intrinsic definition of strong shape for paracompact topological spaces is presented. At first a coherent proximate net f:X → Y is defined, indexed by finite subsets of normal coverings of Y, and then there is a homotopy between two coherent proximate nets defined. A definition of composition of classes of homotopies between two coherent proximate nets f : X → Y and g : Y → Z is given. Then it is proved that for any other choice of corresponding coverings, a function is obtained that is in the same class with the previously defined composition. The strong shape category is obtained, with paracompacta as objects, and the homotopy classes of coherent proximate nets as morphisms.

2010 Mathematics Subject Classification.   55P55, 54C56, 55Q07.

Key words and phrases.   Coherent proximate net, covering, homotopy class, strong shape.

DOI: 10.3336/gm.52.2.10

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