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Computability on Subsets of Locally Compact Spaces

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Theory and Applications of Models of Computation (TAMC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4484))

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Abstract

In this paper we investigate aspects of effectivity and computability on closed and compact subsets of locally compact spaces. We use the framework of the representation approach, TTE, where continuity and computability on finite and infinite sequences of symbols are defined canonically and transferred to abstract sets by means of notations and representations. This work is a generalization of the concepts introduced in [4] and [22] for the Euclidean case and in [3] for metric spaces. Whenever reasonable, we transfer a representation of the set of closed or compact subsets to locally compact spaces and discuss its properties and their relations to each other.

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Authors and Affiliations

  1. Nanjing University, China

    Yatao Xu

  2. University of Hagen, Germany

    Tanja Grubba

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  1. Yatao Xu
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  2. Tanja Grubba
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Editor information

Jin-Yi Cai S. Barry Cooper Hong Zhu

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© 2007 Springer-Verlag Berlin Heidelberg

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Xu, Y., Grubba, T. (2007). Computability on Subsets of Locally Compact Spaces. In: Cai, JY., Cooper, S.B., Zhu, H. (eds) Theory and Applications of Models of Computation. TAMC 2007. Lecture Notes in Computer Science, vol 4484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72504-6_9

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  • DOI: https://doi.org/10.1007/978-3-540-72504-6_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72503-9

  • Online ISBN: 978-3-540-72504-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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