کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5777832 | 1633059 | 2017 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The projective Menger property and an embedding of SÏ into function spaces
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: The projective Menger property and an embedding of SÏ into function spaces The projective Menger property and an embedding of SÏ into function spaces](/preview/png/5777832.png)
چکیده انگلیسی
For a Tychonoff space X, we denote by Cp(X) the space of all real-valued continuous functions on X with the topology of pointwise convergence. In this paper, we show that (1) Cp(X,I) is projectively Menger if and only if X is b-discrete (i.e., every countable subset of X is closed and Câ-embedded in X), (2) there is a Menger space L such that the sequential fan SÏ can be embedded into Cp(L). The first (1) enables us to give a direct proof of Arhangel'skii's theorem [2, Theorem 6]: If Cp(X) is Menger, then X is finite. The second (2) is an affirmative answer to Arhangel'skii's problem [5, Problem II.2.7] under CH (the continuum hypothesis).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 220, 1 April 2017, Pages 118-130
Journal: Topology and its Applications - Volume 220, 1 April 2017, Pages 118-130
نویسندگان
Masami Sakai,