θ-R-continuous functions

Abstract

A strong form of continuity, called θ-R-continuity, is introduced. It is shown that θ-R-continuity is stronger than R-continuity. Relationships between θ-R-continuity and various closed graph properties are investigated. Additional properties of θ-R-continuous functions are established.

Keywords

• θ-R-continuity
• R-continuity
• closed graph property
• θ-C-closed
• almost-regular.