Ideal analogues of some variants of the Hurewicz property

Abstract

In this paper, we continue the study on the ideal analogues of several variations of the Hurewicz property introduced by Das et al. [4, 6, 7] for example, the I-Hurewicz (IH), the star I-Hurewicz (SIH), the weakly I-Hurewicz (WIH) and the weakly star-I-Hurewicz (WSIH). It is shown that several implications in the relationship diagram of their concepts are reversible under certain conditions, for instance; (1) If a paracompact Hausdorff space has the WSIHproperty, then it has theWIHproperty. (2) If the complement of dense set has the IHproperty, then theWIHproperty implies the IHproperty and (3) If the complement of dense set has the SIH property, then the WSIH property implies the SIH property. In addition, we introduce the ideal analogues of some new variations of the Hurewicz property called the mildly I-Hurewicz and the star K-I-Hurewicz properties and explore their relationships with other variants of the I-Hurewicz property. We also study the preservation properties under certain mappings.