Non-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers are fundamental, is a fast-growing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry. This book is the first to provide a comprehensive treatment of non-Archimedean locally convex spaces. The authors provide a clear exposition of the basic theory, together with complete proofs and new results from the latest research. A guide to the many illustrative examples provided, end-of-chapter notes and glossary of terms all make this book easily accessible to beginners at the graduate level, as well as specialists from a variety of disciplines.
Background
Advanced age is a well-known risk factor for poor prognosis in COVID-19. However, few studies have specifically focused on very old inpatients with COVID-19. This study aims to describe the clinical characteristics of very old inpatients with COVID-19 and identify risk factors for in-hospital mortality at admission.
Methods
We conducted a nationwide, multicenter, retrospective, observational study in patients ≥80 years hospitalized with COVID-19 in 150 Spanish hospitals (SEMI-COVID-19) Registry (March 1–May 29, 2020). The primary outcome was in-hospital mortality. A uni- and multivariate logistic regression was performed to assess predictors of mortality at admission.
Results
2,772 consecutive patients (49.4% men, median age 86.3 years) were analyzed. Rates of atherosclerotic cardiovascular disease, diabetes mellitus, dementia, and Barthel Index <60 were 30.8%, 25.6%, 30.5%, and 21.0%, respectively. The overall case-fatality rate was 46.9% (n:1,301) and increased with age (80-84 years:41.6%; 85-90 years:47.3%; 90-94 years:52.7%; ≥95 years:54.2%). After analysis, male sex and moderate-to-severe dependence were independently associated with in-hospital mortality; comorbidities were not predictive. At admission, independent risk factors for death were: SatO2 <90%; temperature ≥37.8ºC; qSOFA score ≥2; and unilateral-bilateral infiltrates on chest X-rays. Some analytical findings were independent risk factors for death, including eGFR <45 ml/min/1.73m 2; lactate dehydrogenase ≥500 U/L; CRP ≥80 mg/L; neutrophils ≥7.5x10 3/μL; lymphocytes <0.8x10 3/μL; and monocytes <0.5 x 10 3/μL.
Conclusions
This first large, multicenter cohort of very old inpatients with COVID-19 shows that age, male sex, and poor pre-admission functional status—not comorbidities—are independently associated with in-hospital mortality. Severe COVID-19 at admission is related to poor prognosis.
Some non-archimedean bounded approximation properties are introduced and studied in this paper. As an application, an affirmative answer is given, for non-spherically complete base fields, to the following problem, posed in [13], p. 95: Does there exist an absolutely convex edged set B in a non-archimedean locally convex space such that its closure B is not edged?
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