TY - JOUR
T1 - Topological ordered C- (resp. I-)spaces and generalized metric spaces
AU - Künzi, Hans Peter A.
AU - Mushaandja, Zechariah
PY - 2009/12/1
Y1 - 2009/12/1
N2 - The following result due to Hanai, Morita, and Stone is well known: Let f be a closed continuous map of a metric space X onto a topological space Y. Then the following statements are equivalent: (i) Y satisfies the first countability axiom; (ii) for each y ∈ Y, f- 1 {y} has a compact boundary in X; (iii) Y is metrizable. In this article we obtain several related results in the setting of topological ordered spaces. In particular we investigate the upper and lower topologies of metrizable topological ordered spaces which are both C- and I-spaces in the sense of Priestley.
AB - The following result due to Hanai, Morita, and Stone is well known: Let f be a closed continuous map of a metric space X onto a topological space Y. Then the following statements are equivalent: (i) Y satisfies the first countability axiom; (ii) for each y ∈ Y, f- 1 {y} has a compact boundary in X; (iii) Y is metrizable. In this article we obtain several related results in the setting of topological ordered spaces. In particular we investigate the upper and lower topologies of metrizable topological ordered spaces which are both C- and I-spaces in the sense of Priestley.
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U2 - 10.1016/j.topol.2008.12.040
DO - 10.1016/j.topol.2008.12.040
M3 - Article
AN - SCOPUS:70349466203
SN - 0166-8641
VL - 156
SP - 2914
EP - 2922
JO - Topology and its Applications
JF - Topology and its Applications
IS - 18
ER -