On I-Baire spaces

Abstract

In this paper, the concept of I-Baire spaces is introduced, and characterizations and properties of these spaces are given. It is shown that (X, τ) is Baire if and only if (X, τ, I) is I-Baire for any ideal I on X.

New types of connectedness and intermediate value theorem in ideal topological spaces

“…For example, the Cantor-Bendixson Theorem is generalized in [6]. New special spaces such as I-Rothberger [7], I-Baire [17], I-Resolvable and I-Hyperconnected [3],I-Extremally Disconnected [12], I-Alexandroff and I g -Alexandroff [4] are defined by using ideal. In addition, the concepts of ideal and local function are studied in fuzzy set theory [28], soft set theory [11] and ditopological texture spaces [15].…”

New topologies from obtained operators via weak semi-local function and some comparisons

“…Janković and Hamlett developed well-known results in ideal topological spaces and obtained new results [9]. Apart from all these studies, many special ideal topological spaces were defined by using the concepts of ideal and local function such as J-Baire spaces [14], J-Alexandroff and J -Alexandroff spaces [5], J-Extremally disconnected spaces [10], J-Resolvable spaces and J-Hyperconnected spaces [4], J-Rothberger spaces [7].…”

Generalized Nowhere Dense Sets in Cluster Topological Setting

“…They have a wider application and its progress can find in [6], [7], [10]. The paper can be considered as a continuation of [5] where some cluster topological notions were introduced and it corresponds with the efforts to generalize the Baire classification of sets and the Baire category theorem [4], [11].…”