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On computably locally compact Hausdorff spaces

Published online by Cambridge University Press:  01 February 2009

YATAO XU  and
TANJA GRUBBA
YATAO XU
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, P.R. China Email: yataoxu@gmail.com
TANJA GRUBBA
Affiliation:
Department of Mathematics and Computer Science, University of Hagen, Hagen 58097, Germany Email: Tanja.Grubba@fernuni-hagen.de
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Abstract

Locally compact Hausdorff spaces generalise Euclidean spaces and metric spaces from ‘metric’ to ‘topology’. But does the effectivity on the latter (Brattka and Weihrauch 1999; Weihrauch 2000) still hold for the former? In fact, some results will be totally changed. This paper provides a complete investigation of a specific kind of space – computably locally compact Hausdorff spaces. First we characterise this type of effective space, and then study computability on closed and compact subsets of them. 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.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 19 , Special Issue 1: Theory and Applications of Models of Computation (TAMC) , February 2009 , pp. 101 - 117
Copyright
Copyright © Cambridge University Press 2009

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