Name
Abstract | ||
|---|---|---|
We investigate a hierarchy of representations of topological spaces by measurable functions that extends the traditional notion of admissible representations common to computable analysis. Specific instances of these representations already occur in the literature (for example, the naive Cauchy representation of the reals and the ``jumpu0027u0027 of a representation), and have been used in investigating the computational properties of discontinuous functions. Our main contribution is the integration of a recently developing descriptive set theory for non-metrizable spaces that allows many previous results to generalize to arbitrary countably based $T_0$ topological spaces. In addition, for a class of topological spaces that include the reals (with the Euclidean topology) and the power set of $\omega$ (with the Scott-topology), we give a complete characterization of the functions that are (topologically) realizable with respect to the level of the representations of the domain and codomain spaces. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.4230/OASIcs.CCA.2009.2264 | CCA |
Field | DocType | Volume |
Discrete mathematics,Codomain,Topological space,Pure mathematics,Measurable function,Descriptive set theory,Euclidean topology,Power set,Topological tensor product,Mathematics,Computable analysis | Conference | 11 |
Citations | PageRank | References |
1 | 0.39 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| de brecht | 1 | 128 | 10.77 |
| Akihiro Yamamoto | 2 | 135 | 26.84 |