engleski

Chainable and Circularly Chainable Co-Recursively Enumerable Sets

We investigate under what conditions a co- recursively enumerable set S in R^n is recursive. The topological type of S plays an important role in view of this task. We first examine co-r.e. sets with disconnected complement, and then we focus on study of chainable and circularly chainable continua which are co-r.e. as subsets of R^n. We prove that each co-r.e. circularly chainable continuum which is not chainable must be recursive. This means, for example, that each co-r.e. set in R^n which has topological type of the Warsaw circle or the dyadic solenoid must be recursive. We also prove that for each chainable continuum S which is decomposable and each epsilon >0 there exists a recursive subcontinuum of S which is epsilon-close to S.

Recursive set; Co-recursively enumerable set; Chainable continuum; Circularly chainable continuum

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