Izvorni znanstveni članak

https://doi.org/10.3336/gm.57.1.07

The finite coarse shape - inverse systems approach and intrinsic approach

Ivan Jelić ; Faculty of Science, University of Split, 21 000 Split, Croatia
Nikola Koceić Bilan orcid.org/0000-0003-4430-0091 ; Faculty of Science, University of Split, 21 000 Split, Croatia

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Sažetak

Given an arbitrary category \(\mathcal{C}\), a category \(pro^{*^f}\)-\(\mathcal{C}\) is constructed such that the known \(pro\)-\(\mathcal{C}\) category may be considered as a subcategory of \(pro^{*^f}\)-\(\mathcal{C}\) and that \(pro^{*^f}\)-\(\mathcal{C}\) may be considered as a subcategory of \(pro^*\)-\(\mathcal{C}\). Analogously to the construction of the shape category \(Sh_{(\mathcal{C},\mathcal{D})}\) and the coarse category \(Sh^*_{(\mathcal{C},\mathcal{D})}\), an (abstract) finite coarse shape category \(Sh^{*^f}_{(\mathcal{C},\mathcal{D})}\) is obtained. Between these three categories appropriate faithful functors are defined. The finite coarse shape is also defined by an intrinsic approach using the notion of the \(\epsilon\)-continuity. The isomorphism of the finite coarse shape categories obtained by these two approaches is constructed. Besides, an overview of some basic properties related to the notion of the \(\epsilon\)-continuity is given.

Ključne riječi

Topological space, metric space, ANR, category, homotopy, shape, \(\epsilon\)-continuity

Hrčak ID:

279802

URI

https://hrcak.srce.hr/279802

Datum izdavanja:

28.6.2022.

Posjeta: 610 *