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On the openness of continuous averagings

โœ Scribed by A. Clausing

Publisher
Springer
Year
1978
Tongue
English
Weight
194 KB
Volume
24
Category
Article
ISSN
0025-2611

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๐Ÿ“œ SIMILAR VOLUMES

On linear continuous open surjections of
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Solving a problem by Arkhangel'skii, we construct a linear continuous open surjection L : C,(X) --) C,(Y) for compacta X and Y with 0 < dim X < dim Y < co. An example of nonopen linear continuous surjection of the space C,[O, I] onto itself is given. Related topics and results are discussed.

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The property of openness of an aggregation operator is introduced to indicate that there always exists the possibility of adding some argument value that will change the aggregated value. We then show the incompatibility of openness with the property of associativity.