K-Trivial Closed Sets and Continuous Functions

George Barmpalias,Douglas Cenzer,Jeffrey B. Remmel,Rebecca Weber

conference on computability in europe（2009）

引用 7|浏览7

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摘要

We investigate the notion of K-triviality for closed sets and continuous functions. Every K-trivial closed set contains a K-trivial real. There exists a K-trivial $\Pi^0_1$ class with no computable elements. For any K-trivial degree d, there is a K-trivial continuous function of degree d.

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关键词

continuous function,closed set,computable element,k-trivial degree,k-trivial continuous function,continuous functions,k-trivial closed sets

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