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The Minimal Structures for T A
Author(s) -
McCLUSKEY A. E.,
McCARTAN S. D.
Publication year - 1992
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1992.tb32257.x
Subject(s) - network topology , comparison of topologies , set (abstract data type) , lattice (music) , topology (electrical circuits) , complete lattice , order (exchange) , mathematics , computer science , discrete mathematics , combinatorics , general topology , topological space , physics , extension topology , universality (dynamical systems) , finance , quantum mechanics , acoustics , economics , programming language , operating system
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.