Characterizations of some near-continuous functions and near-open functions
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⫅C1 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-continu...
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| Format: | Article |
| Language: | English |
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Wiley
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171286000856 |
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| _version_ | 1832563601296064512 |
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| author | C. W. Baker |
| author_facet | C. W. Baker |
| author_sort | C. W. Baker |
| collection | DOAJ |
| description | 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⫅C1 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. |
| format | Article |
| id | doaj-art-e557b888d4d548eca1c2e819003275a7 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1986-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e557b888d4d548eca1c2e819003275a72025-02-03T01:13:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-019471572010.1155/S0161171286000856Characterizations of some near-continuous functions and near-open functionsC. W. Baker0Department of Mathematics, Indiana University Southeast, New Albany 47150, Indiana, USAA 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⫅C1 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.http://dx.doi.org/10.1155/S0161171286000856θ-neighborhoodweakly continuous functionθ-continuous functionstrongly θ-continuous functionalmost strongly θ-continuous functionweakly δ-continuous functionweakly open functionalmost open fnctionθ-open functionstrongly θ-open functionalmost strongly θ-open functionweakly δ-open function. |
| spellingShingle | C. W. Baker Characterizations of some near-continuous functions and near-open functions International Journal of Mathematics and Mathematical Sciences θ-neighborhood weakly continuous function θ-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. |
| title | Characterizations of some near-continuous functions and
near-open functions |
| title_full | Characterizations of some near-continuous functions and
near-open functions |
| title_fullStr | Characterizations of some near-continuous functions and
near-open functions |
| title_full_unstemmed | Characterizations of some near-continuous functions and
near-open functions |
| title_short | Characterizations of some near-continuous functions and
near-open functions |
| title_sort | characterizations of some near continuous functions and near open functions |
| topic | θ-neighborhood weakly continuous function θ-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. |
| url | http://dx.doi.org/10.1155/S0161171286000856 |
| work_keys_str_mv | AT cwbaker characterizationsofsomenearcontinuousfunctionsandnearopenfunctions |