Results 221 to 230 of about 6,505 (255)
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Hausdorff Stability of Persistence Spaces
Foundations of Computational Mathematics, 2015Persistence, in the classical case of a topological space \(X\) filtered in sublevel sets by a continuous function \(f:X \to\mathbb{R}\), can be represented by \textit{Persistent Betti Number} (PBN) functions, which are defined on a half-plane, with nonnegative integer values: For each point \((u,v)\) with \(u
Cerri, Andrea, LANDI, Claudia
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Quaestiones Mathematicae, 1979
Abstract A categorical characterization of the category Haus of Hausdorft topological spaces within the category Top of topological spaces is given. A notion of a Hausdorff nearness space is then introduced and it is proved that the resulting subcategory Haus Near of the category Near of nearness spaces fulfills exactly the same characterization as ...
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Abstract A categorical characterization of the category Haus of Hausdorft topological spaces within the category Top of topological spaces is given. A notion of a Hausdorff nearness space is then introduced and it is proved that the resulting subcategory Haus Near of the category Near of nearness spaces fulfills exactly the same characterization as ...
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INFINITE-DIMENSIONAL COMPACT HAUSDORFF SPACES
Mathematics of the USSR-Izvestiya, 1979Various types of infinite dimensionality of compact Hausdorff spaces are studied. In particular, it is shown that the classes of compact Hausdorff spaces for which the small and the large transfinite dimensions are defined coincide. An example, giving a negative solution of Aleksandrov's problem on the coincidence of countable dimensionality and weak ...
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Modal compact Hausdorff spaces
Journal of Logic and Computation, 2012We introduce modal compact Hausdorff spaces as generalizations of modal spaces, and show these are coalgebras for the Vietoris functor on compact Hausdorff spaces. Modal compact regular frames and modal de Vries algebras are introduced as algebraic counterparts of modal compact Hausdorff spaces, and dualities are given for the categories involved ...
Bezhanishvili, G. +2 more
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Inhomogeneous Besov-Hausdorff and Triebel-Lizorkin-Hausdorff Spaces
2010Similarly to [164, Sects. 4, 5] and [165, Sects. 5, 6], in this section, we introduce the inhomogeneous Besov-Hausdorff space \(BH_{p, q}^{s, \tau }({\mathbb{R}}^ n)\) and the Triebel-Lizorkin-Hausdorff space \(FH_{p,q}^{s,\tau } (\mathbb{R}^n )\), whose dual spaces are, respectively, certain Besov-type space and Triebel-Lizorkin-type space when \(p \,\
Wen Yuan, Winfried Sickel, Dachun Yang
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Weakly Closed Functions and Hausdorff Spaces
Mathematische Nachrichten, 1987For \(A\subseteq X\), let \(Cl_{\theta}A=\{x\in X:(Cl U)\cap A\neq \emptyset\) for any open \(U\supseteq \{x\}\}\); A is \(\theta\)-closed if \(A=Cl_{\theta}A\). Two subsets A, B of X are strongly separated if there are open \(U\supseteq A\), \(V\supseteq B\) with (Cl U)\(\cap (Cl V)=\emptyset\).
Rose, D. A., Janković, D. S.
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On ultracoproducts of compact hausdorff spaces
Journal of Symbolic Logic, 1988AbstractI present solutions to several questions of Paul Bankston [2] by means of another version of the ultracoproduct construction, and explain the relation of ultracoproduct of compact Hausdorff spaces to other constructions combining topology, algebra and logic.
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Responsive materials architected in space and time
Nature Reviews Materials, 2022Xiaoxing Xia +2 more
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The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
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Multifunctional biomolecule nanostructures for cancer therapy
Nature Reviews Materials, 2021Jing Wang, Yiye Li, Guangjun Nie
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