T1 - and T2 axioms for frames

Dowker, C. H.; Strauss, Dona; James, I. M.; Kronheimer, E. H.

doi:10.1017/cbo9781107359925.018

Cited by 13 publications

(13 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The properties N 5 and N 4 are just the standard Completely Normal and Normal. The properties N 2 and C appear in [3] as S 2 and T 1 .…”

Section: Some Historical Remarksmentioning

confidence: 99%

“…(Here I am using the sensible terminology, not the innumerate version which hasRegular = T 1 + T 3 for instance. )It is immediately obvious that Normal and Completely Normal are point-free in that they are lattice theoretic properties of the lattice OS of open sets of S. Building on the analysis in[3], in[9] I produced a lattice theoretic property C = Conjunctive together with a chain…”

mentioning

confidence: 99%

See 1 more Smart Citation

A curious nucleus

Simmons

2010

Journal of Pure and Applied Algebra

View full text Add to dashboard Cite

show abstract

“…The properties N 5 and N 4 are just the standard Completely Normal and Normal. The properties N 2 and C appear in [3] as S 2 and T 1 .…”

Section: Some Historical Remarksmentioning

confidence: 99%

mentioning

confidence: 99%

A curious nucleus

Simmons

2010

Journal of Pure and Applied Algebra

View full text Add to dashboard Cite

show abstract

“…To obtain a property that would coincide with the Hausdorff one in the spatial case, Dowker & Strauss [4] introduced the combination…”

Section: 31mentioning

confidence: 99%

More on Subfitness and Fitness

Picado

Pultr

2014

Appl Categor Struct

View full text Add to dashboard Cite

The concepts of fitness and subfitness (as defined in Isbell [9]) are useful separation properties in point-free topology. The categorical behaviour of subfitness is bad and fitness is the closest modification that behaves well. The separation power of the two, however, differs very substantially and subfitness is transparent and turns out to be useful in its own right. Sort of supplementing the article [20] we present several facts on these concepts and their relation. First the "supportive" role subfitness plays when added to other properties is emphasized. In particular we prove that the numerous Dowker-Strauss type Hausdorff axioms become one for subfit frames. The aspects of fitness as a hereditary subfitness are analyzed, and a simple proof of coreflectivity of fitness is presented. Further, another property, prefitness, is shown to also produce fitness by heredity, in this case in a way usable for classical spaces, which results in a transparent characteristics of fit spaces. Finally, the properties are proved to be independent.

show abstract

“…In this paper we shall show that this is the case provided L is meet-continuous (see Section 1.1). Unlike regular and completely regular locales (see [3,11]), the formulation of regularity axioms in this non-distributive environment requires the existence of an order-reversing involution on L.…”

Section: Introductionmentioning

confidence: 99%

Approximating Orders in Meet-Continuous Lattices and Regularity Axioms in Many Valued Topology

Höhle

Kubiak

2007

Order

View full text Add to dashboard Cite

Positron emission tomography (PET) with 2-deoxy-2[(18)F]-fluoro-D-glucose (FDG) can be used to estimate regional cerebral glucose metabolism (rCMRgluc). FDG-PET studies have shown rCMRgluc to be reduced especially in temporal and parietal cortices in Alzheimer's disease (AD). A previous study on monozygotic twins discordant for AD showed that the rCMRgluc of the non-demented twins is reduced significantly in the lateral temporal and parietal cortices compared to unrelated controls. In this study we examined 9 pairs of dizygotic twins discordant for AD with FDG-PET. The rCMRgluc of the demented twins was 16% lower in the prefrontal cortex (p = 0.04), 20% lower in the hippocampus (p = 0.002) and 15% lower in the lateral temporal cortex (p = 0.003) compared to controls. The non-demented twins showed no such reductions on any cortical region compared to unrelated control subjects. This implies that both genes and environment, and not genes alone, are causative in the pathogenesis of AD.

show abstract

T₁ - and T₂ axioms for frames

Cited by 13 publications

References 0 publications

A curious nucleus

A curious nucleus

More on Subfitness and Fitness

Approximating Orders in Meet-Continuous Lattices and Regularity Axioms in Many Valued Topology

Contact Info

Product

Resources

About