A super-multiplicative inequality for the number of finite unlabeled arbitrary and T₀ topologies

2025/11/21 by Ibtsam A. R. Alroily, Alroily, Ibtsam A. R., Brahim Chaourar +1
Mathematics · #54B10 #Advanced Banach Space Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Point processes and geometric inequalities #Primary 05A20 #Secondary 05A16

paper · pdf · doi:10.48550/arxiv.2511.17263

openalex publication_date 2025/11/21 · openalex created_date 2025/11/25 · openalex updated_date 2026/07/28

Abstract

Let n be a nonnegative integer, and f(n) the number of unlabeled finite topologies on n points. We prove that f(n+m) ≥ f(n) f(m) both for the labeled and unlabeled cases. Moreover, we prove a similar inequality for labeled and unlabeled T₀ topologies.

Citations

• The Free product of Matroids

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