Glasnik Matematicki, Vol. 46, No. 2 (2011), 489-503.

THE COARSE SHAPE PATH CONNECTEDNESS

Nikola Koceić Bilan and Nikica Uglešić

Department of Mathematics, University of Split, Teslina 12/III, 21000 Split, Croatia
e-mail: koceic@pmfst.hr

University of Zadar, Pavlinovićeva bb, 23000 Zadar, Croatia
e-mail: nuglesic@unizd.hr


Abstract.   The bi-pointed coarse shape category of topological spaces is constructed and the notions of a coarse shape path and coarse shape connectedness of a space are naturally introduced. It is proven that the shape path connectedness strictly implies the coarse shape path connectedness even on metrizable compacta. Furthermore, the coarse shape path connectedness on metrizable compacta reduces to ordinary connectedness.

2000 Mathematics Subject Classification.   55P55, 54D05.

Key words and phrases.   Bi-pointed space, ANR, polyhedron, inverse system, resolution, expansion, shape, shape path, coarse shape, weak shape.


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DOI: 10.3336/gm.46.2.17


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