Fibrewise slightly separation axioms

Abstract

The aim of this paper is to look at fibrewise slightly issuances of the more important separation axioms of ordinary topology namely fibrewise said to be fibrewise slightly T₀ spaces, fibrewise slightly T₁ spaces, fibrewise slightly R₀ spaces, fibrewise slightly T₂ spaces, fibrewise slightly functionally T₂ spaces, fibrewise slightly regular spaces, fibrewise slightly completely regular spaces, fibrewise slightly normal spaces. In addition, we announce and confirm many proposals related to these concepts.

Subject Classification:

• 54C08
• 54C10
• 55R70

Keywords:

• Fibrewise topological spaces
• Fibrewise slightly T₀ spaces
• Fibrewise slightly T₁ spaces
• Fibrewise slightly Hausdorff spaces
• Fibrewise slightly regular spaces
• Fibrewise slightly normal spaces