Glasnik Matematicki, Vol. 47, No. 1 (2012), 1-20.

LOCAL COMPUTABILITY OF COMPUTABLE METRIC SPACES AND COMPUTABILITY OF CO-C.E. CONTINUA

Zvonko Iljazović

Abstract.   We investigate conditions on a computable metric space under which each co-computably enumerable set satisfying certain topological properties must be computable. We examine the notion of local computability and show that the result by which in a computable metric space which has the effective covering property and compact closed balls each co-c.e. circularly chainable continuum which is not chainable must be computable can be generalized to computable metric spaces which have the effective covering property and which are locally compact. We also give examples which show that neither of these two assumptions can be omitted.

2010 Mathematics Subject Classification.   03D78.

Key words and phrases.   Computable metric space, computable set, co-c.e. set, local computability, the effective covering property.

DOI: 10.3336/gm.47.1.01

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