A note on fuzzy neighbourhood base spaces

2006 ◽  
Vol 157 (20) ◽  
pp. 2725-2738 ◽  
Author(s):  
G. Elsalamony
Keyword(s):  
Neighbourhood Base

Separating Closed Sets by Continuous Mappings into Developable Spaces

1981 ◽  
Vol 33 (6) ◽  
pp. 1420-1431 ◽  
Author(s):  
Harald Brandenburg
Keyword(s):  
Topological Space ◽  
Double Sequence ◽  
Completely Regular ◽  
Closed Sets ◽  
Continuous Mappings ◽  
Neighbourhood Base ◽  
Image Position ◽  
Metrizable Spaces ◽  
Metrization Theorem ◽  
Developable Spaces

A topological space X is called developable if it has a development, i.e., a sequence of open covers of X such that for each x ∈ X the collection is a neighbourhood base of x, whereThis class of spaces has turned out to be one of the most natural and useful generalizations of metrizable spaces [23]. In [4] it was shown that some well known results in metrization theory have counterparts in the theory of developable spaces (i.e., Urysohn's metrization theorem, the Nagata-Smirnov theorem, and Nagata's “double sequence theorem”). Moreover, in [3] it was pointed out that subspaces of products of developable spaces (i.e., D-completely regular spaces) can be characterized in much the same way as subspaces of products of metrizable spaces (i.e., completely regular T1-spaces).

The order-bound topology on Riesz spaces

1970 ◽  
Vol 67 (3) ◽  
pp. 587-593 ◽  
Author(s):  
Yau-Chuen Wong
Keyword(s):  
Convex Sets ◽  
Vector Lattice ◽  
Positive Cone ◽  
Riesz Space ◽  
Hausdorff Topology ◽  
Riesz Spaces ◽  
Neighbourhood Base ◽  
Solid Hull ◽  
Locally Convex

1. Introduction. Let (X, C) be a Riesz space (or vector lattice) with positive cone C. A subset B of X is said to be solid if it follows from |x| ≤ |b| with b in B that x is in B (where |x| denotes the supremum of x and − x). The solid hull of B (absolute envelope of B in the terminology of Roberts (2)) is denoted to be the smallest solid set containing B, and is denoted by SB. A locally convex Hausdorff topology on (X, C) is called a locally solid topology if admits a neighbourhood-base of 0 consisting of solid and convex sets in X; and (X, C, ), where is a locally solid topology, is called a locally convex Riesz space.

Pseudo-closure operators in fuzzy neighbourhood-base spaces

1992 ◽  
Vol 47 (1) ◽  
pp. 109-116 ◽  
Author(s):  
M.H. Ghanim ◽  
Nehad N. Morsi
Keyword(s):  
Closure Operators ◽  
Neighbourhood Base

scholarly journals Relationship between socioeconomic status and incidence of out-of-hospital cardiac arrest is dependent on age

2020 ◽  
pp. jech-2019-213296
Author(s):  
Martin Jonsson ◽  
Petter Ljungman ◽  
Juho Härkönen ◽  
Ben Van Nieuwenhuizen ◽  
Sidsel Møller ◽  
...  
Keyword(s):  
Socioeconomic Status ◽  
Cardiac Arrest ◽  
Negative Binomial ◽  
Age Groups ◽  
Negative Binomial Regression ◽  
Incidence Rates ◽  
Age Group ◽  
Cross Sectional ◽  
Neighbourhood Base ◽  
Hospital Cardiac Arrest

BackgroundThe association between socioeconomic status (SES) and incidence of out-of-hospital cardiac arrest (OHCA) is not fully understood. The aim of this study was to see if area-level socioeconomic differences, measured in terms of area-level income and education, are associated with the incidence of OHCA, and if this relationship is dependent on age.MethodsWe included OHCAs that occurred in Stockholm County between the 1st of January 2006 and the 31st of December 2017, the victims being confirmed residents (n=10 574). We linked the home address to a matching neighbourhood (base unit) via available socioeconomic and demographic information. Socioeconomic variables and incidence rates were assessed by using cross-sectional values at the end of each year. We used zero-inflated negative binomial regression to calculate incidence rate ratios (IRRs).ResultsAmong 1349 areas with complete SES information, 10 503 OHCAs occurred between 2006 and 2017. The IRR in the highest versus the lowest SES area was 0.61 (0.50–0.75) among persons in the 0–44 age group. Among patients in the 45–64 age group, the corresponding IRR was 0.55 (0.47–0.65). The highest SES areas versus the lowest showed an IRR of 0.59 (0.50–0.70) in the 65–74 age group. In the two highest age groups, no significant association was seen (75–84 age group: 0.93 (0.80–1.08); 85+ age group: 1.05 (0.84–1.23)). Similar crude patterns were seen among both men and women.ConclusionsAreas characterised by high SES showed a significantly lower incidence of OHCA. This relationship was seen up to the age of 75, after which the relationship disappeared, suggesting a levelling effect.

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