Recognition of Finite Bitopological Spaces with Unique Isolated Point by Devi Selvam, Sivaramakrishnan Monikandan

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Miyaoka–Yau inequalities and the topological characterization of certain klt varieties by Greb, Daniel, Kebekus, Stefan, Peternell, Thomas

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Micro $\alpha g $-irresolute Maps in Micro Topological Spaces by Rangasamy Anandhi, Nataraj Balamani

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Surfaces of infinite-type are non-Hopfian by Das, Sumanta, Gadgil, Siddhartha

“…Namely, an oriented surface $\Sigma $ is of finite-type if and only if every proper map $f\colon \,\Sigma \rightarrow \Sigma $ of degree one is homotopic to a homeomorphism.…”
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Noncommutative tensor triangulated categories and coherent frames by Mallick, Vivek Mohan, Ray, Samarpita

“…We further show that there is a homeomorphism between the spectral space of radical thick tensor ideals of a noncommutative tensor triangulated category and the collection of open subsets of its spectrum in the Hochster dual topology.…”
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From homogeneous metric spaces to Lie groups by Cowling, Michael G., Kivioja, Ville, Le Donne, Enrico, Nicolussi Golo, Sebastiano, Ottazzi, Alessandro

“…We study homogeneous metric spaces, by which we mean connected, locally compact metric spaces whose isometry group acts transitively.After a review of a number of classical results, we use the Gleason–Iwasawa–Montgomery–Yamabe–Zippin structure theory to show that for all positive $ \epsilon $, each such space is $ (1,\epsilon ) $-quasi-isometric to a connected metric Lie group (metrized with a left-invariant distance that is not necessarily Riemannian).Next, we develop the structure theory of Lie groups to show that every homogeneous metric manifold is homeomorphically roughly isometric to a quotient space of a connected amenable Lie group, and roughly isometric to a simply connected solvable metric Lie group.Third, we investigate solvable metric Lie groups in more detail, and expound on and extend work of Gordon and Wilson [31, 32] and Jablonski [44] on these, showing, for instance, that connected solvable Lie groups may be made isometric if and only if they have the same real-shadow.Finally, we show that homogeneous metric spaces that admit a metric dilation are all metric Lie groups with an automorphic dilation.…”
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