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On Complete Topological Spaces [PDF]
Transactions of the American Mathematical Society, 1935 DEFINITION I. If M is a space in which there is defined a metric dist (f, g) satisfying the usual postulates for distance ([1], p. 94), then a sequence F: fl, f2, * * * is fundamental if, for every 3>0, there exists an n = nli (3) such that m, n > ni imply dist (fn, f,) 0, there exists an n2 = n2(8) such that n > n2 implies dist (f, f,) < 8.
John von Neumann
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On the Structure of Topological Spaces [PDF]
Axioms, 2022 The structure of topological spaces is analysed here through the lenses of fibrous preorders. Each topological space has an associated fibrous preorder and those fibrous preorders which return a topological space are called spatial.
Nelson Martins-Ferreira
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Tilings in topological spaces [PDF]
International Journal of Mathematics and Mathematical Sciences, 1999 A tiling of a topological space X is a covering of X by sets (called tiles) which are the closures of their pairwise-disjoint interiors. Tilings of ℝ2 have received considerable attention (see [2] for a wealth of interesting examples and results as well ...
F. G. Arenas
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Minimal Topological Spaces [PDF]
Transactions of the American Mathematical Society, 1963 Manuel P. Berri, Manuel P. Berri
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Topological Space-Time Crystal. [PDF]
Physical Review Letters, 2022 We introduce a new class of out-of-equilibrium noninteracting topological phases: the topological space-time crystals. These are time-dependent quantum systems that do not have discrete spatial translation symmetries but instead are invariant under ...
Yang Peng
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Fuzzy metric topology space and manifold [PDF]
Journal of Fuzzy Extension and Applications, 2023 This paper, considers the fuzzy topological subsets, fuzzy topological spaces and introduces a novel concept of fuzzy Hausdorff space and fuzzy manifold space in this regards. Based on these concepts, we present a concept of fuzzy metric Hausdorff spaces
Mahdi Mollaei Arani
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Topological natures of the Gauss-Bonnet black hole in AdS space [PDF]
Physical Review D, 2022 In the recent proposal [Phys. Rev. Lett. 129, 191101 (2022)], the black holes were viewed as topological thermodynamic defects by using the generalized off-shell free energy.
Cong-xin Liu, Jin Wang
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Topological transformation and free-space transport of photonic hopfions [PDF]
Advanced Photonics, 2022 Structured light fields embody strong spatial variations of polarisation, phase and amplitude. Understanding, characterization and exploitation of such fields can be achieved through their topological properties.
Yijie Shen +5 more
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Topological Photonic Crystals: Physics, Designs, and Applications [PDF]
Laser & Photonics reviews, 2022 Recent research in topological photonics has not only proposed and realized novel topological phenomena such as one‐way broadband propagation and robust transport of light, but also designed and fabricated photonic devices with high‐performance indexes ...
Guo-Jing Tang +5 more
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\(\mathcal{I}^{\mathcal{K}}\)-SEQUENTIAL TOPOLOGY
Ural Mathematical Journal, 2023 In the literature, \(\mathcal{I}\)-convergence (or convergence in \(\mathcal{I}\)) was first introduced in [11]. Later related notions of \(\mathcal{I}\)-sequential topological space and \(\mathcal{I}^*\)-sequential topological space were introduced and ...
H. S. Behmanush, M. Küçükaslan
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