A generalization of Čech-complete spaces and Lindelöf Σ\Sigma -spaces

summary:The class of $s$-spaces is studied in detail. It includes, in particular, all Čech-complete spaces, Lindelöf $p$-spaces, metrizable spaces with the weight $\leq 2^\omega$, but countable non-metrizable spaces and some metrizable spaces are not in it. It is shown that $s$-spaces are in a duality with Lindelöf $\Sigma$-spaces: $X$ is an $s$-space if and only if some (every) remainder of $X$ in a compactification is a Lindelöf $\Sigma$-space [Arhangel'skii A.V., Remainders of metrizable and close to metrizable spaces, Fund. Math. {220} (2013), 71--81]. A basic fact is established: the weight and the networkweight coincide for all $s$-spaces. This theorem generalizes the similar statement about Čech-complete spaces. We also study hereditarily $s$-spaces, provide various sufficient conditions for a space to be a hereditarily $s$-space, and establish that every metrizable space has a dense subspace which is a hereditarily $s$-space. It is also shown that every dense-in-itself compact hereditarily $s$-space is metrizable

Antibody- and T Cell-Dependent Responses Elicited by a SARS-CoV-2 Adenoviral-Based Vaccine in a Socially Vulnerable Cohort of Elderly Individuals

Background: In spite of compelling evidence demonstrating safety and immunogenicity of adenoviral-based SARS-CoV-2 vaccines in the general population, its effects in socially vulnerable elderly individuals are poorly understood. Here we aimed to investigate the efficacy of two doses of combined vector vaccine, the Gam-COVID-Vac (Sputnik-V vaccine), at 14, 42, and 180 days after immunization, in a nursing home for underprivileged population and homeless individuals. Methods: A phase 3, open-label clinical trial involving administration of two adenoviral vectors (Ad26-Ad5) vaccine, in elderly individuals over the ages of 60 years was performed. SARS-CoV-2 Spike RBD-specific IgG antibodies at days 21-, 42- and 180 post-vaccination was analyzed in sera of individuals receiving two doses of the Sputnik-V vaccine with an interval of 21 days. SARS-CoV-2-specific CD8+ T cell responses, measured by intracellular tumor necrosis factor (TNF) was determined by flow cytometry following antigen-specific cultures. Results: A total of 72 elderly adults with a mean age of 72.6 ± 9.5 years-old was selected after applying the inclusion criteria, all corresponding to an underprivileged population. Two-doses vaccination with Sputnik-V vaccine elicited an antibody-mediated immune response (revealed by quantitative detection of SARS-CoV-2-specific IgG antibodies, CMIA) 70% at day 21, 90% at day 42, and 66.1% at day 180. Fully vaccinated individuals had robust SARS-CoV-2-specific T cell responses, evidenced by TNF production in CD4+ and CD8+ T cells in all time periods analyzed. Conclusion: Six months after receipt of the second dose of the Gam-COVID-Vac vaccine, SARS-CoV-2-specific IgG levels declined substantially among the tested population, whereas CD4+ and CD8+ T-cell-mediated immunity remained at high levels. These data suggest that two doses of combined adenoviral-based vaccine elicits a considerable level of SARS-CoV-2 immune responses in elderly individuals, highlighting its safety and immunogenicity in this highly vulnerable population

Cozero Complemented Spaces; When the Space of Minimal Prime Ideals of a C(X) is Compact

If X is a Tychonoff space, C(X) its ring of real-valued continuous functions, and f C(X), then the cozeroset of f is coz(f)= {xX: f(x)≠0}. If, for every cozeroset V of X, there is a disjoint cozeroset V′ such that V V′ is dense in X, then X is said to be cozero complemented. It has long been known that X is cozero complemented iff the space MinC(X) of minimal prime ideals of C(X) (in the hull-kernel or Zariski topology) is compact iff the classical ring of fractions of C(X) is von Neumann regular. While many characterizations of cozero complemented spaces are known, they seem not to be adequate to answer some natural questions about them raised by R. Levy and J. Shapiro in an unpublished preprint. These questions concern the relationship between a space being cozero complemented and certain kinds of subspaces having this property, and between a product of two spaces being cozero complemented and the factor spaces being cozero complemented. Also, some conditions are given that guarantee that a space that is locally cozero complemented has this property globally. In this paper partial answers are given to these questions. Sample results: If X is weakly Lindelöf and dense in T, then X is cozero complemented iff T is cozero complemented; if X×Y is weakly Lindelöf and cozero complemented, then X and Y are cozero complemented, but if D is an uncountable discrete space, then βD×βD is not cozero complemented even though βD is cozero complemented. If X is locally cozero complemented and either weakly Lindelöf or paracompact, then X is cozero complemented