2016/04/07 by Maya Altınok, Oleksiy Dovgoshey, Altinok, Maya +3
Mathematics · #28A05 #Advanced Banach Space Theory #Advanced Topology and Set Theory #Classical Analysis and ODEs (math.CA) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1604.02049
openalex publication_date 2016/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For subsets of \mathbb R+ = [0,∞) we introduce a notion of coherently porous sets as the sets for which the upper limit in the definition of porosity at a point is attained along the same sequence. We prove that the union of two strongly porous at 0 sets is strongly porous if and only if these sets are coherently porous. This result leads to a characteristic property of the intersection of all maximal ideals containing in the family of strongly porous at 0 subsets of \mathbb R+. It is also shown that the union of a set A ⊆ \mathbb R+ with arbitrary strongly porous at 0 subset of \mathbb R+ is porous at 0 if and only if A is lower porous at 0.