Unions and ideals of locally strongly porous sets

For subsets of ${\mathbb{R}}^{+}=[0,\mathrm{\infty })$ 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 $A \subseteq \mathbb R^+$witharbitrarystronglyporousat$0$subsetof$\mathbb R^+$isporousat$0$ifandonlyif$A$islowerporousat$0$.