TY - JOUR
ID - 123052
TI - Topological characterization of chainable sets and chainability via continuous functions
JO - Khayyam Journal of Mathematics
JA - KJM
LA - en
SN -
AU - Rezaei, Gholam Reza
AU - Asadzadeh, Mohammad Sina
AU - Jamalzadeh, Javad
AD - Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
AD - Department of Mathematics, University of Sistan and Baluchestan, Zahedan,
Iran.
Y1 - 2021
PY - 2021
VL - 7
IS - 1
SP - 77
EP - 85
KW - ϵ-chainable
KW - function-f-chainable
KW - ultrapseudocompact
DO - 10.22034/kjm.2020.219320.1710
N2 - 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.
UR - https://www.kjm-math.org/article_123052.html
L1 - https://www.kjm-math.org/article_123052_e4c5804fe16f5bd6826091dbe093035d.pdf
ER -