More on cellular-Lindelöf spaces

Xuan, Wei-Feng; Song, Yan-Kui

doi:10.1016/j.topol.2019.106861

Cited by 8 publications

(15 citation statements)

References 10 publications

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“…5, we also consider two more general properties, those of cellular-countable-compactness and cellularsequential-compactness, both of which imply pseudocompactness. We show that a Urysohn first countable cellular-countably-compact space is countably compact and using the results of this section we answer a question posed in [16] concerning cellular-Lindelöf spaces.…”

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confidence: 77%

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On cellular-compactness and related properties

Alas

Junqueira

Passos

et al. 2020

RACSAM

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We study three subclasses of the class of pseudocompact spaces. We answer two open questions concerning cellular-compact spaces and another concerning cellular-Lindelöf spaces and introduce and study three other subclasses of the class of feebly compact spaces, namely the class of cellular-countably-compact spaces, that of the cellular-sequentially-compact spaces and that of the cellular-compact-metrizable spaces. We show that it is independent of ZFC whether or not a cellular-compact-metrizable L OT S is metrizable.

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confidence: 77%

“…Question 3.14 of [16] asks whether or not the product of a cellular-Lindelöf space and a compact space is cellular-Lindelöf. Theorem 5.4 allows us to answer this question in the negative.…”

Section: Theorem 54mentioning

confidence: 99%

On cellular-compactness and related properties

Alas

Junqueira

Passos

et al. 2020

RACSAM

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“…The key point of our proof is to show that any first countable Hausdorff cellular-compact space A. BELLA is weakly Lindelöf with respect to closed sets. This gives a positive answer to Question 5.18 in [14] within the class of first countable spaces. Then, the cardinality bound valid for Urysohn spaces can be easily deduced from a theorem of Alas [1].…”

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confidence: 79%

“…On the other hand, any countable discrete space is strongly cellular-Lindelöf but not cellular-compact. We are now ready to give a partial positive answer to Question 5.18 of [14]. Our proof is inspired by the argument used in Theorem 4.13 of [16].…”

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confidence: 99%

“…According to [5], a space X is cellular-Lindelöf if for any disjoint collection of non-empty open sets U there is a Lindelöf subspace L such that L ∩ U = ∅ for each U ∈ U. This notion has been further investigated in [6], [11], [12], [14] and [15]. Among other things, in [6] it was shown that if 2 <c = c, then the cardinality of a normal first countable cellular-Lindelöf space does not exceed c.…”

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confidence: 99%

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On cellular-compact and related spaces

Bella

2020

Topology and its Applications

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Tkachuk and Wilson proved that a regular first countable cellular-compact space has cardinality not exceeding the continuum. In the same paper they asked if this result continues to hold for Hausdorff spaces. Xuan and Song considered the same notion and asked if every cellular-compact space is weakly Lindelöf. We answer the last question for first countable spaces. As a byproduct of this result, we present a somewhat different proof of Tkachuk and Wilson theorem, valid for the wider class of Urysohn spaces. The result actually holds for a class of spaces in between cellular-compact and cellular-Lindelöf. We conclude with some comments on the cardinality of a weakly linearly Lindelöf space.2010 Mathematics Subject Classification. 54A25, 54D20, 54D55.

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