Products of convergence properties
János Gerlits, Zsigmond Nagy (1982)
Commentationes Mathematicae Universitatis Carolinae
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János Gerlits, Zsigmond Nagy (1982)
Commentationes Mathematicae Universitatis Carolinae
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Aleksander V. Arhangel'skii (2010)
Commentationes Mathematicae Universitatis Carolinae
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Some strong versions of the Fréchet-Urysohn property are introduced and studied. We also strengthen the concept of countable tightness and generalize the notions of first-countability and countable base. A construction of a topological space is described which results, in particular, in a Tychonoff countable Fréchet-Urysohn space which is not first-countable at any point. It is shown that this space can be represented as the image of a countable metrizable space under a continuous pseudoopen...
J. Chaber (1976)
Fundamenta Mathematicae
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Aleksander V. Arhangel'skii, Angelo Bella (1996)
Commentationes Mathematicae Universitatis Carolinae
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Countable tightness is compared to the stronger notion of countable fan-tightness. In particular, we prove that countable tightness is equivalent to countable fan-tightness in countably compact regular spaces, and that countable fan-tightness is preserved by pseudo-open compact mappings. We also discuss the behaviour of countable tightness and of countable fan-tightness under the product operation.
Oleg Okunev (2013)
Open Mathematics
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We prove that the one-point Lindelöfication of a discrete space of cardinality ω 1 is homeomorphic to a subspace of C p (X) for some hereditarily Lindelöf space X if the axiom [...] holds.