Characterizations of some near-continuous functions and near-open functions

C. W. Baker

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-6

Abstract:

A subset N of a topological space is defined to be a θ -neighborhood of x if there exists an open set U such that x ∈ U ⫅ C 1 U ⫅ N . This concept is used to characterize the following types of functions: weakly continuous, θ -continuous, strongly θ -continuous, almost strongly θ -continuous, 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.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:563506

DOI: 10.1155/S0161171286000856

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