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Top-designs in the category of Fort spaces

Mehrnaz Pourattar, Fatemah Ayatollah Zadeh Shirazi

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 $λ$ and Top--design $C-(X,D,λ)$ of type $i$?" for $i=1,2,3,4$. We prove there exist $λ$ and $C-(X,D,λ)$, Top--design of type 2 (resp. type 4) if and only if $C$ can be embedded into $D$.

Top-designs in the category of Fort spaces

Abstract

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

Paper Structure

This paper contains 2 sections, 7 theorems, 8 equations.

Table of Contents

  1. Introduction
  2. Results in Top-designs on $X$

Key Result

Lemma 2.1

For $U,V\subseteq X$ with $U\approx V$ and $X\setminus U\approx X\setminus V$ we have:

Theorems & Definitions (14)

  • Lemma 2.1
  • proof
  • Theorem 2.2
  • proof
  • Lemma 2.3
  • proof
  • Theorem 2.4
  • proof
  • Theorem 2.5
  • proof
  • ...and 4 more