1
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
2
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
10.22034/kjm.2020.219320.1710
Abstract
In the last decade, the notions of function-f-ϵ-chainability, uniformly function-f-ϵ-chainability, function-f-ϵ-chainable sets and locally functionf-chainable sets were studied in some papers. We show that the notions of function-f-ϵ-chainability and uniformly function-f-ϵ-chainability are equivalent to the notion of non-ultrapseudocompactness in topological spaces. Also, all of these are equivalent to the condition that each pair of non-empty subsets (resp., subsets with non-empty interiors) is function-f-ϵ-chainable (resp., locally function-f-chainable). Further, we provide a criterion for connectedness with covers. In the paper "Characterization of ϵ-chainable sets in metric spaces" (Indian J. Pure Appl. Math. 33 (2002), no. 6, 933{940), the chainability of a pair of subsets in a metric space has been defined wrongly and consequently Theorem 1 and Theorem 5 are found to be wrong. We rectify their definition appropriately and consequently, we give appropriate results and counterexamples.
Rezaei, G., Asadzadeh, M., Jamalzadeh, J. (2021). Topological characterization of chainable sets and chainability via continuous functions. Khayyam Journal of Mathematics, 7(1), 77-85. doi: 10.22034/kjm.2020.219320.1710
MLA
Gholam Reza Rezaei; Mohammad Sina Asadzadeh; Javad Jamalzadeh. "Topological characterization of chainable sets and chainability via continuous functions". Khayyam Journal of Mathematics, 7, 1, 2021, 77-85. doi: 10.22034/kjm.2020.219320.1710
HARVARD
Rezaei, G., Asadzadeh, M., Jamalzadeh, J. (2021). 'Topological characterization of chainable sets and chainability via continuous functions', Khayyam Journal of Mathematics, 7(1), pp. 77-85. doi: 10.22034/kjm.2020.219320.1710
VANCOUVER
Rezaei, G., Asadzadeh, M., Jamalzadeh, J. Topological characterization of chainable sets and chainability via continuous functions. Khayyam Journal of Mathematics, 2021; 7(1): 77-85. doi: 10.22034/kjm.2020.219320.1710