rc-continuous functions and functions with rc-strongly closed graph
The family of regular closed subsets of a topological space is used to introduce two concepts concerning a function f from a space X to a space Y. The first of them is the notion of f being rc-continuous. One of the established results states that a space Y is extremally disconnected if and only if...
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203203410 |
| Summary: | The family of regular closed subsets of a topological space is
used to introduce two concepts concerning a function f from a
space X to a space Y. The first of them is the notion of f
being rc-continuous. One of the established results states that a
space Y is extremally disconnected if and only if each
continuous function from a space X to Y is rc-continuous. The
second concept studied is the notion of a function f having an
rc-strongly closed graph. Also one of the established results
characterizes rc-compact spaces (≡S-closed spaces) in
terms of functions that possess rc-strongly closed graph. |
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| ISSN: | 0161-1712 1687-0425 |