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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171296000427 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |