ACADSTAFF UGM
| Title | : | A New Convergence Inducing the SI-Topology |
| Author | : |
Hadrian Andradi, M.Sc., Ph.D. (1) Chong Shen (2) Weng Kin Ho (3) Dongsheng Zhao (4) |
| Date | : | 2018 |
| Keyword | : | SI-convergence, SI-topology, I-continuous space, SI-continuous space SI-convergence, SI-topology, I-continuous space, SI-continuous space |
| Abstract | : | In their attempt to develop domain theory in situ T0 spaces, Zhao and Ho introduced a new topology defined by irreducible sets of a resident topological space, called the SI-topology. Notably, the SI-topology of the Alexandroff topology of posets is exactly the Scott topology, and so the SI-topology can be seen as a generalisation of the Scott topology in the context of general T0 spaces. It is well known that the convergence structure that induces the Scott topology is the Scott-convergence – also known as lim-inf convergence by some authors. Till now, it is not known which convergence structure induces the SI-topology of a given T0 space. In this paper, we fill in this gap in the literature by providing a convergence structure, called the SI-convergence structure, that induces the SI-topology. Additionally, we introduce the notion of I-continuity that is closely related to the SI-convergence structure, but distinct from the existing notion of SI-continuity (introduced by Zhao and Ho earlier). For SI-continuity, we obtain here some equivalent conditions for it. Finally, we give some examples of non-Alexandroff SI-continuous spaces. |
| Group of Knowledge | : | Matematika |
| Original Language | : | English |
| Level | : | Internasional |
| Status | : |
Published
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