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Digitale Medien

Generalizing semidistributivity (1993)

Geyer, Winfried

Springer

Order 10 (1993), S. 77-92

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ISSN: 1572-9273

Schlagwort(e): 06B05 ; 06B20 ; Doubling construction ; semidistributive lattices ; k-semidistributivity ; context ; doubling classes ; pseudovariety

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Abstract A latticeL is called congruence normal if it can be generated by doubling of convex sets starting with the one-element lattice. In the special case of intervals, the lattice is called bounded. It has been proven thatL is bounded if and only ifL is congruence normal and semidistributive. In this paper we study the connection between certain classes of convex sets and generalized semidistributive laws. These so-called doubling classes are pseudovarieties which can be described by implications as well as by forbiden substructures. In the end, we examine the structure of the lattice of all doubling classes.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01108710

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Digitale Medien

On context patterns associated with concept lattices (1993)

Geyer, Winfried

Springer

Order 10 (1993), S. 363-373

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ISSN: 1572-9273

Schlagwort(e): 06B05 ; 06A15 ; Context ; arrow relation ; concept lattice ; context pattern ; strictly realizable context pattern

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Abstract In this paper, we consider the following reconstruction problem: Given two ordered sets (G, ≤) and (M, ≤) representing join- and meet-irreducible elements, respectively together with three relationsJ, , $${\hbox{\ \hbox{$\mid$}\kern -1em\lower .5em \hbox{$\leftarrow$}}} $$ onG×M modelling comparability (g≤m) and maximal noncomparability with respect tog (g≰m, butg≤m*) and with respect tom (g≰m, butg≤m*). We determine necessary and sufficient conditions for the existence of a finite latticeL and injections α:G→J(L) and β:M→M(L) such that the given order relations and the abstract relations coincide with the one induced by the latticeL.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01108830

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Digitale Medien

African urbanization in Metropolitan South Africa — differential urbanization perspectives (1993)

Geyer, Hermanus S.

Springer

GeoJournal 30 (1993), S. 301-308

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ISSN: 1572-9893

Quelle: Springer Online Journal Archives 1860-2000

Thema: Geographie

Notizen: Abstract The supersession of the process of urbanization by what has been termed “polarization reversal” and “counterurbanization” in advanced developing and developed countries has become a much debated issue over the past 15 years. Disaggregated migration studies indicate that in addition to mainstream population migration patterns, undercurrent migration patterns may be evident which could differ quite substantially from the former. Such divergent migratory patterns occurring at the same time in the same country are called “differential urbanization”. As a potentially important urban development policy consideration, attention is focused in this paper on differential urbanization trends in South Africa at the metropolitan level. Recent informal urban settlement patterns of the African population within the major metropolitan areas are contrasted against these differential urbanization trends to determine the implications of both for residential development in the metropolitan areas during the post-apartheid era.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF00806721

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