On Weak Forms of Open and Closed Functions via (₁, ₂) -open Sets

Key Points

• Weakly open functions are characterized within the context of tau1 tau2 beta open sets, providing new insights.
• The study explores the definitions of weakly closed functions, focusing on their relationship to tau1 tau2 beta closed sets.
• Several characterizations of these functions are presented, offering a deeper understanding of open and closed functions.
• Implications for topology are discussed, highlighting the importance of these weak forms in functional analysis.