2019/04/08 by Takayuki Kihara, Kihara, Takayuki, Keng Meng Ng +3 · 2 citations
Computer Science · Mathematics · #03D28 #54A05 #54D10 #54G20 #54H05 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Logic in Computer Science (cs.LO) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1904.04107
openalex publication_date 2019/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The enumeration degrees of sets of natural numbers can be identified with the degrees of difficulty of enumerating neighborhood bases of points in a universal second-countable T0-space (e.g. the ω-power of the Sierpiński space). Hence, every represented second-countable T0-space determines a collection of enumeration degrees. For instance, Cantor space captures the total degrees, and the Hilbert cube captures the continuous degrees by definition. Based on these observations, we utilize general topology (particularly non-metrizable topology) to establish a classification theory of enumeration degrees of sets of natural numbers.