Characterization of posets for order-convergence being topological

In: Mathematica Slovaca, vol. 68, no. 1

Tao Sun - Qingguo Li

Detaily:

Rok, strany: 2018, 11 - 20

Kľúčové slová:

poset, order-convergence, topology, doubly continuous poset, $\mathcal{R^{\ast}}$-doubly continuous poset

DOI: https://doi.org/10.1515/ms-2017-0075

O článku:

We study a basic problem: in what posets is the order-convergence topological? We introduce the notion of $\mathcal{R^*}$-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 $\mathcal{R^*}$-doubly continuous. This is the main result which can be regarded as a complete characterization of posets for the order-convergence being topological.

Ako citovať:

ISO 690:

Sun, T., Li, Q. 2018. Characterization of posets for order-convergence being topological. In Mathematica Slovaca, vol. 68, no.1, pp. 11-20. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0075

APA:

Sun, T., Li, Q. (2018). Characterization of posets for order-convergence being topological. Mathematica Slovaca, 68(1), 11-20. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0075

O vydaní:

Publikované: 23. 2. 2018