Naslov
Computability of Products of Chainable Continua

Autori
Čelar, Matea ; Iljazović, Zvonko

Izvornik
Theory of computing systems (1432-4350) 65 (2021); 410-427

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Computable topological space ; Computable set ; Semicomputable set ; Product of chainable continua

Sažetak
We examine conditions under which a semicomputable set in a computable topological space is computable. In particular, we examine topological pairs (A, B) with the following property: if X is a computable topological space and f:A→X is an embedding such that f(A) and f(B) are semicomputable sets in X, then f(A) is a computable set in X. Such pairs (A, B) are said to have computable type. It is known that (K, {; ; ; ; a, b}; ; ; ; ) has computable type if K is a Hausdorff continuum chainable from a to b. It is also known that (In, ∂In) has computable type, where In is the n-dimensional unit cube and ∂In is its boundary in Rn. We generalize these results by proving the following: if Ki is a nontrivial Hausdorff continuum chainable from ai to bi for i∈{; ; ; ; 1, …, n}; ; ; ; , then (∏ni=1Ki, B) has computable type, where B is the set of all (x1, …, xn)∈∏ni=1Ki such that xi ∈{; ; ; ; ai, bi}; ; ; ; for some i∈{; ; ; ; 1, …, n}; ; ; ; .

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Računarstvo

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