2017 Fiscal Year Final Research Report
Research on complete quasi-metric spaces with algebraic structure
| Project/Area Number |
15K15940
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Theory of informatics
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| Research Institution | Kyoto University (2016-2017)
National Institute of Information and Communications Technology (2015) |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | quasi-Polish space / topological algebra / semilattices / powerspace |
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| Outline of Final Research Achievements |
This research investigated interactions between algebraic and topological structure on a class of topological spaces called quasi-Polish spaces (i.e., countably based completely quasi-metrizable spaces). Quasi-Polish spaces generalize Polish spaces (which are often used in analysis and measure theory), omega-continuous domains (which are used in theoretical computer science), and countably based spectral spaces (which are used in algebraic geometry and logic). This research mainly focused on algebraic structures known as semilattices, which have important applications in mathematical logic and theoretical computer science.
Our main accomplishments include a careful analysis of several powerspace monads on the category of quasi-Polish spaces which provide a category-theoretical approach (via Eilenberg-Moore algebras) to studying quasi-Polish semilattices. We have also made many new contributions to the general theory of quasi-Polish spaces, which is still a very young research area.
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| Free Research Field |
mathematical logic, topology, computation
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