Coding Polish spaces
Diego Alejandro Mej\'ia
TL;DR
This paper introduces a coding method for Polish metric spaces using countable metric spaces, analyzes the complexity of related statements and relations, and proposes a coding scheme for continuous functions between these spaces.
Contribution
It develops a new coding framework for Polish metric spaces and continuous functions, enabling complexity analysis of related mathematical statements.
Findings
Coding simplifies the analysis of Polish spaces.
Complexity of statements varies with coding methods.
Proposes a new coding scheme for continuous functions.
Abstract
We use countable metric spaces to code Polish metric spaces and evaluate the complexity of some statements about these codes and of some relations that can be determined by the codes. Also, we propose a coding for continuous functions between Polish metric spaces.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Coding theory and cryptography