Top-designs in the category of Fort spaces

TL;DR

This paper investigates the existence of specific top-designs within infinite Fort spaces, establishing conditions under which certain types of designs exist based on subset embeddings.

Contribution

It characterizes when top-designs of types 2 and 4 exist in infinite Fort spaces, linking their existence to the embeddability of subsets.

Findings

Existence of type 2 top-designs if and only if C can be embedded into D.

Existence of type 4 top-designs if and only if C can be embedded into D.

Provides conditions for the existence of top-designs of types 1 and 3 (not specified).

Abstract

In infinite topological Fort space $X$, for nonempty subsets $C,D$ of $X$ in the following text we answer to this question "Is there any $\lambda$ and Top--design $C-(X,D,\lambda)$ of type $i$?" for $i=1,2,3,4$. We prove there exist $\lambda$ and $C-(X,D,\lambda)$, Top--design of type 2 (resp. type 4) if and only if $C$ can be embedded into $D$.