engleski

Computability of pseudo-cubes

We examine topological pairs (Δ, Σ) which have computable type: if X iscomputable topological space and f : Δ → X a topological embedding such that f (Δ) and f (Σ) are semicomputable sets in X, then f (Δ) is a computable set in X. It is known that (D, W ) has computable type, where D is the Warsaw disc and W is the Warsaw circle. In this paper we identify a class of topological pairs which are similar to (D, W ) and have computable type: we prove that (Δ, Σ) has computable type if Δ can somehow be approximated by a 2-cell whose boundary circle approximates Σ. Moreover, we examine higher-dimensional analogues of such pairs.

Computable topological space ; Computable set ; Semicomputable set ; Pseudo-square ; Pseudo-cube

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