Sequences and related closure and compactness properties in frames

Mark Sioen; David Holgate; Jacques Masuret

doi:10.1016/j.topol.2021.107912

Sequences and related closure and compactness properties in frames

Mark Sioen, David Holgate, Jacques Masuret

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The aim of this note is to introduce concepts of sequence and sequence convergence in the point-free setting. These are then used to define sequential closedness and associated compactness properties in frames. The interplay of these closure and compactness notions are investigated. Relating back to the pointed setting provides additional insight into an asymmetric Kuratowski-Mrówka type theorem for countable compactness in general topology.

Originele taal-2	English
Artikelnummer	107912
Aantal pagina's	12
Tijdschrift	Topology and its Applications
Volume	309
DOI's	https://doi.org/10.1016/j.topol.2021.107912
Status	Published - 15 mrt. 2022

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© 2021 Elsevier B.V.

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title = "Sequences and related closure and compactness properties in frames",

abstract = "The aim of this note is to introduce concepts of sequence and sequence convergence in the point-free setting. These are then used to define sequential closedness and associated compactness properties in frames. The interplay of these closure and compactness notions are investigated. Relating back to the pointed setting provides additional insight into an asymmetric Kuratowski-Mr{\'o}wka type theorem for countable compactness in general topology.",

author = "Mark Sioen and David Holgate and Jacques Masuret",

note = "Funding Information: This work was supported by the South African National Research Foundation and the authors' respective universities. Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

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AU - Holgate, David

AU - Masuret, Jacques

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N2 - The aim of this note is to introduce concepts of sequence and sequence convergence in the point-free setting. These are then used to define sequential closedness and associated compactness properties in frames. The interplay of these closure and compactness notions are investigated. Relating back to the pointed setting provides additional insight into an asymmetric Kuratowski-Mrówka type theorem for countable compactness in general topology.

AB - The aim of this note is to introduce concepts of sequence and sequence convergence in the point-free setting. These are then used to define sequential closedness and associated compactness properties in frames. The interplay of these closure and compactness notions are investigated. Relating back to the pointed setting provides additional insight into an asymmetric Kuratowski-Mrówka type theorem for countable compactness in general topology.

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DO - 10.1016/j.topol.2021.107912

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SN - 0166-8641

VL - 309

JO - Topology and its Applications

JF - Topology and its Applications

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Sequences and related closure and compactness properties in frames

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