On dense subspaces satisfying stronger separation axioms

summary:We prove that it is independent of ZFC whether every Hausdorff countable space of weight less than $c$ has a dense regular subspace. Examples are given of countable Hausdorff spaces of weight $c$ which do not have dense Urysohn subspaces. We also construct an example of a countable Urysohn space, which has no dense completely Hausdorff subspace. On the other hand, we establish that every Hausdorff space of $\pi$-weight less than $\mathfrak p$ has a dense completely Hausdorff (and hence Urysohn) subspace. We show that there exists a Tychonoff space without dense normal subspaces and give other examples of spaces without “good” dense subsets

Genetic Diversity of HIV-1 in Krasnoyarsk Krai: Area with High Levels of HIV-1 Recombination in Russia

More than a quarter of HIV-infected individuals registered in Russia live in Siberia. Unlike Central Russia where HIV-1 subtype A6 is predominant, in most Siberian regions since 2012, a new HIV-1 CRF63_02A1 genetic variant has spread, with the share of this variant attaining 75–85% among newly identified HIV cases. Krasnoyarsk Krai is considered to be a high-risk territory according to morbidity rate and HIV infection incidence among the population. The current paper aims to study the molecular epidemiologic characteristics of HIV-1 spreading in Krasnoyarsk Krai. Phylogenetic and recombination analyses of pol (PR-RT, IN) and env regions of the virus were used for genotyping 159 HIV-1 isolated in Krasnoyarsk Krai. 57.2% of the isolates belonged to subtype A (A6) specific to Russia, 12.6% to CRF63_02A1, and 0.6% to CRF02_AGСА, and in 29.6% HIV-1 URFs were detected, including URF63/А (23.9%), URFА/В (4.4%), and URF02/А (1.3%). In 6 of 7, HIV-1 URFА/В identical recombination model was detected; the origin of 38 URF63/А was proven to be the result of individual recombination events. Since 2015, a share of the population with newly diagnosed HIV who were infected with HIV-1 URF reached an exceptionally high rate of 38.6%. As distinct from adjacent Siberian regions, the HIV-1 CRF63_02A1 prevalence rate in Krasnoyarsk Krai is within 16%; however, the increased contribution of new HIV-1 into the regional epidemic development was observed due to the recombination of viruses of subtypes А, В, and CRF63_02A1. The difference between the described molecular epidemiologic picture in Krasnoyarsk Krai and in adjacent areas is likely caused by differences in predominant routes of HIV transmission and by more recent HIV-1 CRF63_02A1 transmission in the PWID group, which had a high prevalence of HIV-1 subtype A by the time of the new virus transmission, resulting in increased possibility of coinfection with various HIV-1 genetic variants