The Minimal Structures for TA

A. E. McCLUSKEY; S. D. McCARTAN

doi:10.1111/j.1749-6632.1992.tb32257.x

The Minimal Structures for T_A

A. E. McCLUSKEY
, S. D. McCARTAN

Mathematics

Queen's University of Belfast

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

1 Citation (Scopus)

Abstract

Given the lattice of all topologies definable for an infinite set X, a technique to solve many minimality problems is developed. Its potential in characterizing and, where possible, identifying those topologies that are minimal with respect to various invariants, including T_A, is illustrated. Finally, an alternative description of each topologically established minimal structure in terms of the behavior of the naturally occurring specialization order and the intrinsic topology on the resulting partially ordered set is offered.

Original language	English
Pages (from-to)	138-155
Number of pages	18
Journal	Annals of the New York Academy of Sciences
Volume	659
Issue number	1
DOIs	https://doi.org/10.1111/j.1749-6632.1992.tb32257.x
Publication status	Published - Sep 1992

Keywords

Alexandroff
Minimal T‐spaces
Scott topologies.
specialization order

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10.1111/j.1749-6632.1992.tb32257.x

Cite this

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abstract = "Given the lattice of all topologies definable for an infinite set X, a technique to solve many minimality problems is developed. Its potential in characterizing and, where possible, identifying those topologies that are minimal with respect to various invariants, including TA, is illustrated. Finally, an alternative description of each topologically established minimal structure in terms of the behavior of the naturally occurring specialization order and the intrinsic topology on the resulting partially ordered set is offered.",

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AB - Given the lattice of all topologies definable for an infinite set X, a technique to solve many minimality problems is developed. Its potential in characterizing and, where possible, identifying those topologies that are minimal with respect to various invariants, including TA, is illustrated. Finally, an alternative description of each topologically established minimal structure in terms of the behavior of the naturally occurring specialization order and the intrinsic topology on the resulting partially ordered set is offered.

KW - Alexandroff

KW - Minimal T‐spaces

KW - Scott topologies.

KW - specialization order

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The Minimal Structures for T_A

Abstract

Keywords

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