## On some types of faint continuity.(English)Zbl 1261.54004

Summary: Using the concept of pre-open sets and semi-open sets, we introduce and investigate two forms of faint continuity which are called faint pre-continuity and faint semi-continuity. We obtain their characterizations, their basic properties and their relationships with other forms of functions between topological spaces. Also some results of Noiri-Popa, El-Atik and Nasef are improved. Finally, we discuss the product of faintly pre-continuous and faintly semi-continuous functions.

### MSC:

 54C08 Weak and generalized continuity 54D10 Lower separation axioms ($$T_0$$–$$T_3$$, etc.) 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
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