Scott convergence and fuzzy Scott topology on L-posets

We firstly generalize the fuzzy way-below relation on an -poset, and consider its continuity by means of this relation. After that, we introduce a kind of stratified -generalized convergence structure on an -poset. In terms of that, -fuzzy Scott topology and fuzzy Scott topology are considered, and...

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Bibliographic Details
Published in:Open mathematics (Warsaw, Poland) Poland), 2017-06, Vol.15 (1), p.815-827
Main Authors: Liu, Hongping, Chen, Ling
Format: Article
Language:English
Subjects:
03E72
06A06
54A40
Convergence
Convergence structure
filter
l-poset
poset
Scott topology
Set theory
Stratified
stratified l-filter
Topology
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Summary:We firstly generalize the fuzzy way-below relation on an -poset, and consider its continuity by means of this relation. After that, we introduce a kind of stratified -generalized convergence structure on an -poset. In terms of that, -fuzzy Scott topology and fuzzy Scott topology are considered, and the properties of fuzzy Scott topology are discussed in detail. At last, we investigate the Scott convergence of stratified -filters on an -poset, and show that an -poset is continuous if and only if the Scott convergence on it coincides with the convergence with respect to the corresponding topological space.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2017-0067