Minimal TUD spaces

[EN] A topological space is TUD if the derived set of each point is the union of disjoint closed sets. We show that there is a minimal TUD space which is not just the Alexandroff topology on a linear order. Indeed the structure of the underlying partial order of a minimal TUD space can be quite complex. This contrasts sharply with the known results on minimality for weak separation axioms.Mccluskey, A.; Watson, S. (2002). Minimal TUD spaces. Applied General Topology. 3(1):55-64. doi:10.4995/agt.2002.211255643

Representing set-inclusion by embeddability (among the subspaces of the real line)

AbstractWe establish that the powerset P(R) of the real line R, ordered by set-inclusion, has the same ordertype as a certain subset of P(R) ordered by homeomorphic embeddability. This is a contribution to the ongoing study of the possible ordertypes of subfamilies of P(R) under embeddability, pioneered by Banach, Kuratowski and Sierpiński

An elementary counterexample on dense normality

AbstractWe show that the Sorgenfrei plane is not normal on any of its dense subsets, that is, is not densely normal. This addresses in the simplest possible terms Arhangel'skii's question as to whether an elementary example exists of a regular κ-normal space that fails to be densely normal

Genome-wide CRISPR–Cas9 screening reveals ubiquitous T cell cancer targeting via the monomorphic MHC class I-related protein MR1

Human leukocyte antigen (HLA)-independent, T cell-mediated targeting of cancer cells would allow immune destruction of malignancies in all individuals. Here, we use genome-wide CRISPR-Cas9 screening to establish that a T cell receptor (TCR) recognized and killed most human cancer types via the monomorphic MHC class I-related protein, MR1, while remaining inert to noncancerous cells. Unlike mucosal-associated invariant T cells, recognition of target cells by the TCR was independent of bacterial loading. Furthermore, concentration-dependent addition of vitamin B-related metabolite ligands of MR1 reduced TCR recognition of cancer cells, suggesting that recognition occurred via sensing of the cancer metabolome. An MR1-restricted T cell clone mediated in vivo regression of leukemia and conferred enhanced survival of NSG mice. TCR transfer to T cells of patients enabled killing of autologous and nonautologous melanoma. These findings offer opportunities for HLA-independent, pan-cancer, pan-population immunotherapies