Remainders of locally Cech-complete spaces and homogeneity

We study remainders of locally Cech-complete spaces. In particular, itis established that if X is a locally Cech-complete non- ech-completespace, then no remainder of X is homogeneous (Theorem 3.1). We alsoshow that if Y is a remainder of a locally Cech-complete space X, andevery y ∈ Y is a Gδ-point in Y , then the cardinality of Y doesn't exceed2 ω. Several other results are obtained.

PDF

___

S.J. Nedev, o-metrizable spaces, Trudy Mosk. Matem. O-va 24 (1971), 201-236.
K. Nagami, Σ-spaces, Fund. Mathematicae 61 (1969), 169-192.
M. Henriksen and J.R. Isbell, Some properties of compactications, Duke Math. J. 25 (1958), 83-106.
R. Engelking, General Topology, PWN, Warszawa, 1977.
E.K. van Douwen, F. Tall, and W. Weiss, Non-metrizable hereditarily Lindelöf spaces with point-countable bases from CH, Proc. Amer. Math. Soc. 64 (1977), 139-145.
A.V. Arhangel'skii and M.M. Choban, Some generalizations of the concept of a p-space, Topology and Appl. 158 (2011), 1381 - 1389.
A.V. Arhangel'skii, A generalization of ech-complete spaces and Lindelöf Σ-spaces, Comment. Math. Universatis Carolinae 54:2 (2013), 121139.
A.V. Arhangel'skii, Remainders of metrizable and close to metrizable spaces, Fundamenta Mathematicae 220 (2013), 7181.
A.V. Arhangel'skii, Remainders of metrizable spaces and a generalization of Lindelöf Σspaces, Fund. Mathematicae 215 (2011), 87-100.
A.V. Arhangel'skii, On a class of spaces containing all metric and all locally compact spaces, Mat. Sb. 67(109) (1965), 55-88. English translation: Amer. Math. Soc. Transl. 92 (1970), 1-39.

Hacettepe Journal of Mathematics and Statistics-Cover

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

Arşiv