Two theorems on measurable sets and sets having the Baire property
On the comparison of the density type topologies generated by sequences and by functions
In the paper we investigate density type topologies generated by functions satisfying condition , which are not generated by any sequence.
Multigeometric sequences and Cantorvals
For a sequence x ∈ l 10, one can consider the achievement set E(x) of all subsums of series Σn=1∞ x(n). It is known that E(x) has one of the following structures: a finite union of closed intervals, a set homeomorphic to the Cantor set, a set homeomorphic to the set T of subsums of Σn=1∞ x(n) where c(2n − 1) = 3/4n and c(2n) = 2/4n (Cantorval). Based on ideas of Jones and Velleman [Jones R., Achievement sets of sequences, Amer. Math. Monthly, 2011, 118(6), 508–521] and Guthrie and Nymann [Guthrie...
On homeomorphisms of the density type topologies
This paper is dealing of the homeomorphisms of the density type topologies introduced in [3].
A note on intersections of certain topologies on R
On similarity between topologies
Let T 1 and T 2 be topologies defined on the same set X and let us say that (X, T 1) and (X, T 2) are similar if the families of sets which have nonempty interior with respect to T 1 and T 2 coincide. The aim of the paper is to study how similar topologies are related with each other.
On some extensions of -finite measures.
Ideal Convergence of Sequences and Some of its Applications
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