Lattice-valued Hahn-Dieudonné-Tong insertion theorem and stratification structure
Liu Ying-Ming,Luo Mao-kang +1 more
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TLDR
In this article, the authors generalize the Hahn-Dieudonne-Tong Insertion Theorem, a classical result on semicontinuous functions, to the case that the ranges are a certain kind of lattices L. The success of the method is based on the study in depth on the topological relations among the stratifications.About:
This article is published in Topology and its Applications.The article was published on 1992-06-19 and is currently open access. It has received 14 citations till now.read more
Citations
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The relation of Banach-Alaoglu theorem and Banach-Bourbaki-Kakutani-Šmulian theorem in complete random normed modules to stratification structure
TL;DR: In this article, it was shown that the classical BBKS theorem does not hold universally for complete random normed modules unless they possess extremely simple stratification structure, namely their supports are essentially purely μ-atomic.
Localic Katÿetov-Tong insertion theorem and localic Tietze extension theorem
Li Yong-ming,Wang Guo-jun +1 more
TL;DR: A localic Katyetov-Tong insertion theorem is given and proved in terms of a localic upper and lower continuous chain over a locale in this paper, and the Urysohn lemma and Tietze extension theorem are shown as applications of the localic insertion theorem.
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Insertion of lattice-valued and hedgehog-valued functions☆
TL;DR: In this paper, it was shown that the Hilbert cube is a ⊲-separable completely distributive lattice and some join-dense subset is both order and topologically isomorphic to the hedgehog J ( ω ) with appropriately defined topology.
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The hyperspace of the regions below of all lattice-value continuous maps and its Hilbert cube compactification
TL;DR: In this paper, the family of all lower closed sets including X x 0 in the product space X x ΛL and ↓ C(X, L) the one of the regions below of all continuous maps from X to L is shown to be homeomorphic to [-1, 1]ω.
Metrizable completely distributive lattices
TL;DR: In this article, the authors studied the topological properties of the interval topology on a completely distributive lattice and showed that a metrizable completely distributable lattice is an ANR if and only if it contains at most finite completely compact elements.
References
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Book
A Compendium of Continuous Lattices
TL;DR: In this article, the authors present a primer of complete lattices and complete topology of continuous lattices, including the Scott topology and meet-continuous lattices.
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Fuzzy topology. II. Product and quotient spaces
Pu Pao-Ming,Liu Ying-Ming +1 more
TL;DR: In this paper, a theory of neighborhood structures and theorems in the theory of Moore-Smith's convergence are generalized to fuzzy topological spaces, including product spaces and quotient spaces.
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Initial and Final Fuzzy Topologies and the Fuzzy Tychonoff Theorem
TL;DR: The notions of initial and final fuzzy topologies are introduced and it is shown that from a categorical point of view they are the right concepts to generalize the topological ones.