Remainders of locally \v{C}ech-complete spaces and homogeneity
Remainders of locally \v{C}ech-complete spaces and homogeneity
We study remainders of locally \v{C}ech-complete spaces. In particular, it is established that if $X$ is a locally \v{C}ech-complete non-\v{C}ech-complete space, then no remainder of $X$ is homogeneous (Theorem 3.1). We also show that if $Y$ is a remainder of a locally \v{C}ech-complete space $X$, and every $y\in Y$ is a $G_\delta$-point in $Y$, then the cardinality of $Y$ doesn't exceed $2^\omega$. Several other results are obtained.
Keywords:
Remainder, Compactification, $G_\delta$-point, Homogeneous, Point-countable base, Lindel\"{o}f $\Sigma$-space, Charming space, Countable type \v{C}ech-complete,
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- Yayın Aralığı: Yılda 6 Sayı
- Başlangıç: 2002
- Yayıncı: Hacettepe Üniversitesi Fen Fakultesi