A characterization of the uniform convergence points set of some convergent sequence of functions

We characterize the uniform convergence points set of a pointwisely convergent sequence of real-valued functions defined on a perfectly normal space. We prove that if X is a perfectly normal space which can be covered by a disjoint sequence of dense subsets and A ⊆ X, then A is the set of points of the uniform convergence for some convergent sequence (fn ) n∈ω of functions fn : X → ℝ if and only if A is Gδ -set which contains all isolated points of X. This result generalizes a theorem of Ján Borsík published in 2019.

Commuting pairs of endomorphisms of

We consider commuting pairs of holomorphic endomorphisms of $\mathbb{P}^{2}$ with disjoint sequence of iterates. The case that has not been completely studied is when their degrees coincide after some number of iterations. We show in this case that they are either commuting Lattès maps or commuting homogeneous polynomial maps of $\mathbb{C}^{2}$ inducing a Lattès map on the line at infinity.

Characterization of a Class of Equicontinuous Sets of Finitely Additive Measures with an Application to Vector Valued Borel Measures

Let V denote a ring of subsets of an abstract space X, let R + denote the nonnegative reals, and let N denote the set of positive integers. We denote by C(V) the space of all subadditive and increasing functions, from the ring V into R +, which are zero at the empty set. The space C(V) is called the space of contents on the ring V and elements are referred to as contents. A sequence of sets An ∊ V, n ∊ N is said to be dominated if there exists a set B ∊ V such that An ⊆ B, for n = 1, 2, A content p ∊ C(V) is said to be Rickart on the ring V if lim n p(An ) = 0 for each dominated, disjoint sequence An ∊ V, n ∊ N.