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

Research output: Contribution to journal › Article › peer-review

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-Mrówka type theorem for countable compactness in general topology.

Original language	English
Article number	107912
Number of pages	12
Journal	Topology and its Applications
Volume	309
DOIs	https://doi.org/10.1016/j.topol.2021.107912
Publication status	Published - 15 Mar 2022

Bibliographical note

Funding Information:
This work was supported by the South African National Research Foundation and the authors' respective universities.

Publisher Copyright:
© 2021 Elsevier B.V.

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10.1016/j.topol.2021.107912

Cite this

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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.",

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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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SN - 0166-8641

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Sequences and related closure and compactness properties in frames

Abstract

Bibliographical note

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