On rectifiable spaces and paratopological groups
نویسندگان
چکیده
منابع مشابه
Lindelöf Σ-Spaces and R-Factorizable Paratopological Groups
We prove that if a paratopological group G is a continuous image of an arbitrary product of regular Lindelöf Σ-spaces, then it is R-factorizable and has countable cellularity. If in addition, G is regular, then it is totally ω-narrow and satisfies celω(G) ≤ ω, and the Hewitt–Nachbin completion of G is again an R-factorizable paratopological group.
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15 صفحه اولA note on the remainders of rectifiable spaces
In this paper, we mainly investigate how the generalized metrizability properties of the remainders affect the metrizability of rectifiable spaces, and how the character of the remainders affects the character and the size of a rectifiable space. Some results in [A. V. Arhangel'skii and J. Van Mill, On topological groups with a first-countable remainder, Topology Proc. 42 (2013...
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In this paper, we prove a dichotomy theorem for remainders in compactifications of paratopological groups: every remainder of a paratopological group $G$ is either Lindel"{o}f and meager or Baire. Furthermore, we give a negative answer to a question posed in [D. Basile and A. Bella, About remainders in compactifications of homogeneous spaces, Comment. Math. Univ. Caroli...
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We present several examples of feebly compact Hausdorff paratopological groups (i.e., groups with continuous multiplication) which provide answers to a number of questions posed in the literature. It turns out that a 2-pseudocompact, feebly compact Hausdorff paratopological group G can fail to be a topological group. Our group G has the Baire property, is Fréchet–Urysohn, but it is not precompa...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2011
ISSN: 0166-8641
DOI: 10.1016/j.topol.2010.12.008