ACADSTAFF UGM
| Title | : | A Topological Scott Convergence Theorem |
| Author | : |
Hadrian Andradi, M.Sc., Ph.D. (1) Weng Kin Ho (2) |
| Date | : | 2019 |
| Keyword | : | Scott convergence,topological convergence,irreducibly derived topology,I-continuous spaces,I-stable spaces,DI spaces Scott convergence,topological convergence,irreducibly derived topology,I-continuous spaces,I-stable spaces,DI spaces |
| Abstract | : | Recently, J. D. Lawson encouraged the domain theory community to consider the scienti?c program of developing domain theory in the wider context of T0 spaces instead of restricting to posets. In this paper, we respond to this calling with an attempt to formulate a topological version of the Scott Convergence Theorem, i.e., an order-theoretic characterisation of those posets for which the Scott-convergence S is topological. To do this, we make use of the ID replacement principle to create topological analogues of well-known domain-theoretic concepts, e.g., I-continuous spaces correspond to continuous posets, as I-convergence corresponds to S-convergence. In this paper, we consider two novel topological concepts, namely, the I-stable spaces and the DI spaces, and as a result we obtain some necessary (respectively, su?cient) conditions under which the convergence structure I is topological. |
| Group of Knowledge | : | Matematika |
| Original Language | : | English |
| Level | : | Internasional |
| Status | : |
Published
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| No | Title | Action |
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| 1 |
a topological scott convergence theorem.pdf
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