Let I ⊆ P(ω) be an ideal. We continue our investigation of the class of spaces with the I-ideal convergence property, denoted (I). We show that if I is an analytic, non-countably generated P-ideal then (I) ⊆ s₀. If in addition I is non-pathological and not isomorphic to , then (I) spaces have measure zero. We also present a characterization of the (I) spaces using clopen covers.
In the paper we obtain several characteristics of pre- of strongly preirresolute topological vector spaces and show that the extreme point of a convex subset of a strongly preirresolute topological vector space lies on the boundary.
Let and be closed subsets of [0,1] with a subset of the limit points of . Necessary and sufficient conditions are found for the existence of a continuous function such that is an -limit set for and is the set of fixed points of in .
For any Borel ideal ℐ we describe the ℐ-Baire system generated by the family of quasi-continuous real-valued functions. We characterize the Borel ideals ℐ for which the ideal and ordinary Baire systems coincide.
The main goal of this paper is to characterize the family of all functions f which satisfy the following condition: whenever g is a Darboux function and f < g on ℝ there is a Darboux function h such that f < h < g on ℝ.
In this article, we investigate new topological descriptions for two well-known mappings and defined on intermediate rings of . Using this, coincidence of each two classes of -ideals, -ideals and -ideals of is studied. Moreover, we answer five questions concerning the mapping raised in [J. Sack, S. Watson, and among intermediate rings, Topology Proc. 43 (2014), 69–82].
The characterization of the pointwise limits of the sequences of Świątkowski functions is given. Modifications of Świątkowski property with respect to different topologies finer than the Euclidean topology are discussed.
We investigate the topological structure of the space 𝓓ℬ₁ of bounded Darboux Baire 1 functions on [0,1] with the metric of uniform convergence and with the p*-topology. We also investigate some properties of the set Δ of bounded derivatives.