TY - JOUR
T1 - Refinable maps in dimension theory
AU - Koyama, Akira
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 1984/6
Y1 - 1984/6
N2 - This paper studies properties of refinable maps and contains applications to dimension theory. It is proved that refinable maps between compact Hausdorff spaces preserve covering dimension exactly and do not raise small cohomological dimension with any coefficient group. The notion of a c-refinable map is introduced and is shown to play a comparable role in the setting of normal spaces. For example, c-refinable maps between normal spaces are shown to preserve covering dimension and S-weak infinite-dimensionality. These facts do not hold for refinable maps.
AB - This paper studies properties of refinable maps and contains applications to dimension theory. It is proved that refinable maps between compact Hausdorff spaces preserve covering dimension exactly and do not raise small cohomological dimension with any coefficient group. The notion of a c-refinable map is introduced and is shown to play a comparable role in the setting of normal spaces. For example, c-refinable maps between normal spaces are shown to preserve covering dimension and S-weak infinite-dimensionality. These facts do not hold for refinable maps.
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U2 - 10.1016/0166-8641(84)90045-2
DO - 10.1016/0166-8641(84)90045-2
M3 - Article
AN - SCOPUS:0000967059
VL - 17
SP - 247
EP - 255
JO - Topology and its Applications
JF - Topology and its Applications
SN - 0166-8641
IS - 3
ER -