Absolutes of Hausdorff spaces and cardinal invariants $F_{\te}$ and $t_{\te}$}

TL;DR

This paper investigates the relationships between various cardinal functions in Hausdorff spaces, extending recent work on $F_{ heta}$ and $t_{ heta}$ for H-closed Urysohn spaces and absolutes.

Contribution

It introduces new results connecting cardinal functions $t$, $t_{ heta}$, $F$, and $F_{ heta}$ within the framework of Iliadis and Banaschewski absolutes of Hausdorff spaces.

Findings

Established basic relationships among the cardinal functions.

Extended the study of $F_{ heta}$ and $t_{ heta}$ to H-closed Urysohn spaces.

Analyzed the interplay of cardinal invariants in the context of space absolutes.

Abstract

This article extends the recent study of the cardinal functions $F_{\theta}$ and $t_{\theta}$ for H-closed Urysohn spaces and the research of I. Bandlov and V.I. Ponomarev on tightness type of absolutes. In particular, basic results are obtained and used to study the relationships among the cardinal functions $t$, $t_{\theta}$, $F$ and $F_{\theta}$ in the context of Iliadis and Banaschewski absolutes of Hausdorff spaces.