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. R., Asadzadeh, M. S., & 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. R., Asadzadeh, M. S., 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. R., Asadzadeh, M. S., 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