TY - JOUR
T1 - Uniform Eberlein compactifications of metrizable spaces
AU - Banakh, Taras
AU - Leiderman, Arkady
PY - 2012/4/15
Y1 - 2012/4/15
N2 - We prove that each metrizable space X (of size |X|≤c) has a (first countable) uniform Eberlein compactification and each scattered metrizable space has a scattered hereditarily paracompact compactification. Each compact scattered hereditarily paracompact space is uniform Eberlein and belongs to the smallest class A of compact spaces, which contains the empty set, the singleton, and is closed under producing the Alexandroff compactification of the topological sum of a family of compacta from the class A.
AB - We prove that each metrizable space X (of size |X|≤c) has a (first countable) uniform Eberlein compactification and each scattered metrizable space has a scattered hereditarily paracompact compactification. Each compact scattered hereditarily paracompact space is uniform Eberlein and belongs to the smallest class A of compact spaces, which contains the empty set, the singleton, and is closed under producing the Alexandroff compactification of the topological sum of a family of compacta from the class A.
KW - Hereditarily paracompact space
KW - Metrizable space
KW - Scattered compactification
KW - Scattered space
KW - Uniform Eberlein compact space
UR - http://www.scopus.com/inward/record.url?scp=84857999392&partnerID=8YFLogxK
U2 - https://doi.org/10.1016/j.topol.2011.06.060
DO - https://doi.org/10.1016/j.topol.2011.06.060
M3 - Article
SN - 0166-8641
VL - 159
SP - 1691
EP - 1694
JO - Topology and its Applications
JF - Topology and its Applications
IS - 7
ER -