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- Title
Unions and ideals of locally strongly porous sets.
- Authors
ALTINOK, Maya; DOVGOSHEY, Oleksiy; KÜÇÜKASLAN, Mehmet
- Abstract
For subsets of 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 00 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 contained in the family of strongly porous at 00 subsets of ℝ+. It is also shown that the union of a set A⊆R+A⊆ℝ+ with arbitrary strongly porous at 00 set is porous at 00 if and only if AA is lower porous at 00.
- Subjects
POROSITY; MAXIMAL ideals; POROUS materials; INFINITESIMAL geometry; MATHEMATICAL analysis
- Publication
Turkish Journal of Mathematics, 2017, Vol 41, Issue 6, p1510
- ISSN
1300-0098
- Publication type
Article
- DOI
10.3906/mat-1604-44