Anqie entropy and arithmetic compactification of natural numbers
نویسندگان
چکیده
To study arithmetic structures of natural numbers, we introduce a notion entropy functions, called anqie entropy. This possesses some crucial properties common to both Shannon's and Kolmogorov's entropies. We show that all functions with zero form C*-algebra. Its maximal ideal space defines our compactification which is totally disconnected but not extremely disconnected. also compute the $K$-groups continuous on compactification. As an application, any topological dynamical system $\lambda$, can be approximated by symbolic systems less than or equal $\lambda$.
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ژورنال
عنوان ژورنال: Banach Journal of Mathematical Analysis
سال: 2021
ISSN: ['1735-8787', '2662-2033']
DOI: https://doi.org/10.1007/s43037-021-00162-6