CHARACTERIZATIONS OF SOME NEAR-CONTINUOUS FUNCTIONS AND NEAR-OPEN FUNCTIONS

C. W. BAKER

《International Journal of Mathematics and Mathematical Sciences》 1986卷 (1986/12) Pp. 715-720

https://doi.org/10.1155/S0161171286000856

摘要

A subset N of a topological space is defined to be a θ-nelghborhood of x if there exists an open set U such that x ε U⊆ C1 U⊆ N. This concept is used to characterize the following types of functions: weakly continuous, θ-contlnuous, strongly θ-continuous, almost strongly θ-cbntinuous, weakly δ-continuous, weakly open and almost open functions. Additional characterizations are given for weakly δ-continuous functions. The concept of θ-neighborhood is also used to define the following types of open maps: θ-open, strongly θ-open, almost strongly θ-open, and weakly δ-open functions.

關鍵字

θ-neighborhood ； weakly continuous function ； -continuous function ； strongly θ-continuous function ； almost strongly θ-continuous function ； weakly δ-continuous function ； weakly open function ； almost open fnction ； θ-open function ； strongly θ-open function ； almost strongly θ-open function ； weakly δ-open function