Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904063 | Topology and its Applications | 2018 | 10 Pages |
Abstract
Sapirovskii [16] proved that |X|â¤ÏÏ(X)c(X)Ï(X), for a regular space X. We introduce the θ-pseudocharacter of a Urysohn space X, denoted by Ïθ(X), and prove that the previous inequality holds for Urysohn spaces replacing the bounds on cellularity c(X)â¤Îº and on pseudocharacter Ï(X)â¤Îº with a bound on Urysohn cellularity Uc(X)â¤Îº (which is a weaker condition because Uc(X)â¤c(X)) and on θ-pseudocharacter Ïθ(X)â¤Îº respectively (note that in general Ï(â
)â¤Ïθ(â
) and in the class of regular spaces Ï(â
)=Ïθ(â
)). Further, in [6] the authors generalized the Dissanayake and Willard's inequality: |X|â¤2aLc(X)Ï(X), for Hausdorff spaces X[21], in the class of n-Hausdorff spaces and de Groot's result: |X|â¤2hL(X), for Hausdorff spaces [10], in the class of T1 spaces (see Theorems 2.22 and 2.23 in [6]). In this paper we restate Theorem 2.22 in [6] in the class of n-Urysohn spaces and give a variation of Theorem 2.23 in [6] using new cardinal functions, denoted by UW(X), Ïwθ(X), θ-aL(X), hθ-aL(X), θ-aLc(X) and θ-aLθ(X). In [5] the authors introduced the Hausdorff point separating weight of a spaceX denoted by Hpsw(X) and proved a Hausdorff version of Charlesworth's inequality |X|â¤psw(X)L(X)Ï(X)[7]. In this paper, we introduce the Urysohn point separating weight of a spaceX, denoted by Upsw(X), and prove that |X|â¤Upsw(X)θ-aLc(X)Ï(X), for a Urysohn space X.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Fortunata Aurora Basile, Maddalena Bonanzinga, Nathan Carlson,