Function spaces and contractive extensions in Approach Theory: The role of regularity

Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to convergence-approach spaces. Characterizations are obtained for two alternative extensions of regularity to convergence-approach spaces: regularity and strong regularity. The results improve upon what is known even in the convergence case. On the way, a new notion of strictness for convergence-approach spaces is introduced.Comment: previous version had an error, fixed here with a new definition of strictnes

Normality in terms of distances and contractions

The main purpose of this paper is to explore normality in terms of distances between points and sets. We prove some important consequences on realvalued contractions, i.e. functions not enlarging the distance, showing that as in the classical context of closures and continuous maps, normality in terms of distances based on an appropriate numerical notion of $\gamma$-separation of sets, has far reaching consequences on real valued contractive maps, where the real line is endowed with the Euclidean metric. We show that normality is equivalent to (1) separation of $\gamma$-separated sets by some Urysohn contractive map, (2) to Kat\v{e}tov-Tong's interpolation, stating that for bounded positive realvalued functions, between an upper and a larger lower regular function, there exists a contractive interpolating map and (3) to Tietze's extension theorem stating that certain contractions defined on a subspace can be contractively extended to the whole space. The appropriate setting for these investigations is the category of approach spaces, but the results have (quasi)-metric counterparts in terms of non-expansive maps. Moreover when restricted to topological spaces, classical normality and its equivalence to separation by a Urysohn continuous map, to Kat\v{e}tov-Tong's interpolation for semicontinuous maps and to Tietze's extension theorem for continuous maps are recovered

Increased baseline body weight is a risk factor associated with virological failure while on antiretroviral treatment

Mexico AIDS Conference 200

Positive Outcomes of HAART at 24 Months in HIV-Infected Patients in Cambodia.

OBJECTIVES: African and Asian cohort studies have demonstrated the feasibility and efficacy of HAART in resource-poor settings. The long-term virological outcome and clinico-immunological criteria of success remain important questions. We report the outcomes at 24 months of antiretroviral therapy (ART) in patients treated in a Médecins Sans Frontières/Ministry of Health programme in Cambodia. METHODS: Adults who started HAART 24 +/- 2 months ago were included. Plasma HIV-RNA levels were assessed by real-time polymerase chain reaction. Factors associated with virological failure were analysed using logistic regression. RESULTS: Of 416 patients, 59.2% were men; the median age was 33.6 years. At baseline, 95.2% were ART naive, 48.9% were at WHO stage IV, and 41.6% had a body mass index less than 18 kg/m. The median CD4 cell count was 11 cells/microl. A stavudine-lamivudine-efavirenz-containing regimen was initiated predominantly (81.0%). At follow-up (median 23.8 months), 350 (84.1%) were still on HAART, 53 (12.7%) had died, six (1.4%) were transferred, and seven (1.7%) were lost to follow-up. Estimates of survival were 85.5% at 24 months. Of 346 tested patients, 259 (74.1%) had CD4 cell counts greater than 200 cells/microl and 306 (88.4%) had viral loads of less than 400 copies/ml. Factors associated with virological failure at 24 months were non-antiretroviral naive, an insufficient CD4 cell gain of less than 350 cells/microl or a low trough plasma ART concentration. In an intention-to-treat analysis, 73.6% of patients were successfully treated. CONCLUSION: Positive results after 2 years of advanced HIV further demonstrate the efficacy of HAART in the medium term in resource-limited settings

Why have socio-economic explanations between favoured over cultural ones in explaining the intensive spread of HIV in South Africa?

The HIV prevalence in South Africa’s various racial/ethnic groups differs by more than an order of magnitude. These differences are determined not by the lifetime number of sexual partners, but by how these partnerships are more likely to be arranged concurrently in African communities. The available evidence demonstrates that neither HIV nor concurrency rates are determined by socio-economic factors. Rather, high concurrency rates are maintained by a culturally sanctioned tolerance of concurrency. Why then do socio-economicexplanations trump cultural ones in the South African HIV aetiological literature? In this article, we explore how three factors (a belief in monogamy as a universal norm, HIV’s emergence in a time of the construction of non-racialism, and a simplified understanding of HIV epidemiology) have intersected to produce this bias and therefore continue to hinder the country’s HIV prevention efforts