Computable Banach Spaces via Domain Theory 1
نویسنده
چکیده
This paper extends the domain-theoretic approach to computable analysis to complete metric spaces and Banach spaces. We employ the domain of formal balls to deene a computability theory for complete metric spaces. For Banach spaces, the domain specialises to the domain of closed balls, ordered by reversed inclusion. We characterise computable linear operators as those which map computable sequences to computable sequences and are eeectively bounded. We show that the domain-theoretic computability theory is equivalent to the well-established approach by Pour-El & Richards.
منابع مشابه
Computable Banach Spaces via
This paper extends the order-theoretic approach to computable analysis via continuous domains to complete metric spaces and Banach spaces. We employ the domain of formal balls to deene a computability theory for complete metric spaces. For Banach spaces, the domain specialises to the domain of closed balls, ordered by reversed inclusion. We characterise computable linear operators as those whic...
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