Characterization of posets for order-convergence being topological
-
Tao Sun
and
Qingguo Li
Abstract
We study a basic problem: in what posets is the order-convergence topological? We introduce the notion of 𝓡∗-doubly continuous posets, which extends the notion of doubly continuous posets, and then prove that the order-convergence in a poset is topological if and only if the poset is 𝓡∗-doubly continuous. This is the main result which can be regarded as a complete characterization of posets for the order-convergence being topological.
This work was supported by the Natural Science Foundation of China, Grant No. 11371130, and the Natural Science Foundation of Guangxi, Grant No. 2014GXNSFBA118015.
Acknowledgements
We would like to thank the anonymous referee and Prof. Vladimír Olejček for their careful reading and valuable comments which have improved the quality of this paper.
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© 2018 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- On the number of cycles in a graph
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- Classification of posets using zero-divisor graphs
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- Nuclear operators on Cb(X, E) and the strict topology
- More on cyclic amenability of the Lau product of Banach algebras defined by a Banach algebra morphism
- Matrix generalized (θ, ϕ)-derivations on matrix Banach algebras
- Nonlinear ∗-Jordan triple derivations on von Neumann algebras
- Addendum to “A sequential implicit function theorem for the chords iteration”, Math. Slovaca 63(5) (2013), 1085–1100
- Comparison of density topologies on the real line
- Rational homotopy of maps between certain complex Grassmann manifolds
- Examples of random fields that can be represented as space-domain scaled stationary Ornstein-Uhlenbeck fields
- Rothe’s method for physiologically structured models with diffusion
- Zero-divisor graphs of lower dismantlable lattices II
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