کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4661524 1344433 2007 24 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On one-point metrizable extensions of locally compact metrizable spaces
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
On one-point metrizable extensions of locally compact metrizable spaces
چکیده انگلیسی

For a non-compact metrizable space X, let E(X) be the set of all one-point metrizable extensions of X, and when X is locally compact, let EK(X) denote the set of all locally compact elements of E(X) and be the order-anti-isomorphism (onto its image) defined in [M. Henriksen, L. Janos, R.G. Woods, Properties of one-point completions of a non-compact metrizable space, Comment. Math. Univ. Carolin. 46 (2005) 105–123; in short HJW]. By definition λ(Y)=⋂n<ωclβX(Un∩X)\X, where Y=X∪{p}∈E(X) and {Un}n<ω is an open base at p in Y. We characterize the elements of the image of λ as exactly those non-empty zero-sets of βX which miss X, and the elements of the image of EK(X) under λ, as those which are moreover clopen in βX\X. This answers a question of [HJW]. We then study the relation between E(X) and EK(X) and their order structures, and introduce a subset ES(X) of E(X). We conclude with some theorems on the cardinality of the sets E(X) and EK(X), and some open questions.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 154, Issue 3, 1 February 2007, Pages 698-721