Open AccessIdeal analogues of some variants of the Hurewicz property
Author(s) -
Kirti Tyagi,
Sumit Singh,
Manoj Bhardwaj
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1909725t
Subject(s) - paracompact space , mathematics , ideal (ethics) , property (philosophy) , hausdorff space , complement (music) , star (game theory) , set (abstract data type) , pure mathematics , mathematical analysis , computer science , chemistry , law , gene , philosophy , biochemistry , programming language , epistemology , complementation , political science , phenotype
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.