Contra-continuous functions and strongly S-closed spaces
In 1989 Ganster and Reilly [6] introduced and studied the notion of LC-continuous functions via the concept of locally closed sets. In this paper we consider a stronger form of LC-continuity called contra-continuity. We call a function f:(X,τ)→(Y,σ) contra-continuous if the preimage of every open se...
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| Format: | Article |
| Language: | English |
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Wiley
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171296000427 |
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| _version_ | 1832563068518793216 |
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| author | J. Dontchev |
| author_facet | J. Dontchev |
| author_sort | J. Dontchev |
| collection | DOAJ |
| description | In 1989 Ganster and Reilly [6] introduced and studied the notion of LC-continuous
functions via the concept of locally closed sets. In this paper we consider a stronger form of
LC-continuity called contra-continuity. We call a function f:(X,τ)→(Y,σ) contra-continuous if the
preimage of every open set is closed. A space (X,τ) is called strongly S-closed if it has a finite dense
subset or equivalently if every cover of (X,τ) by closed sets has a finite subcover. We prove that contra-continuous
images of strongly S-closed spaces are compact as well as that contra-continuous, β-continuous images of S-closed spaces are also compact. We show that every strongly S-closed space
satisfies FCC and hence is nearly compact. |
| format | Article |
| id | doaj-art-0c5818ebdda74344b59690111b8d7b0e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0c5818ebdda74344b59690111b8d7b0e2025-02-03T01:21:01ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251996-01-0119230331010.1155/S0161171296000427Contra-continuous functions and strongly S-closed spacesJ. Dontchev0Department of Mathematics, University of Helsinki, Helsinki 10 00014, FinlandIn 1989 Ganster and Reilly [6] introduced and studied the notion of LC-continuous functions via the concept of locally closed sets. In this paper we consider a stronger form of LC-continuity called contra-continuity. We call a function f:(X,τ)→(Y,σ) contra-continuous if the preimage of every open set is closed. A space (X,τ) is called strongly S-closed if it has a finite dense subset or equivalently if every cover of (X,τ) by closed sets has a finite subcover. We prove that contra-continuous images of strongly S-closed spaces are compact as well as that contra-continuous, β-continuous images of S-closed spaces are also compact. We show that every strongly S-closed space satisfies FCC and hence is nearly compact.http://dx.doi.org/10.1155/S0161171296000427strongly S-closedclosed covercontra-continuousLC-continuous perfectly continuousstrongly continuousFCC. |
| spellingShingle | J. Dontchev Contra-continuous functions and strongly S-closed spaces International Journal of Mathematics and Mathematical Sciences strongly S-closed closed cover contra-continuous LC-continuous perfectly continuous strongly continuous FCC. |
| title | Contra-continuous functions and strongly S-closed spaces |
| title_full | Contra-continuous functions and strongly S-closed spaces |
| title_fullStr | Contra-continuous functions and strongly S-closed spaces |
| title_full_unstemmed | Contra-continuous functions and strongly S-closed spaces |
| title_short | Contra-continuous functions and strongly S-closed spaces |
| title_sort | contra continuous functions and strongly s closed spaces |
| topic | strongly S-closed closed cover contra-continuous LC-continuous perfectly continuous strongly continuous FCC. |
| url | http://dx.doi.org/10.1155/S0161171296000427 |
| work_keys_str_mv | AT jdontchev contracontinuousfunctionsandstronglysclosedspaces |