Modified continuity and a generalisation of Michael's selection theorem |
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Authors: | J R Giles and M O Bartlett |
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Institution: | (1) Department of Mathematics, University of Newcastle, 2308, NSW, Australia |
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Abstract: | We modify the definitions of continuity and lower semicontinuity for single-valued mappings and upper and lower semicontinuity for set-valued mappings. For single-valued mappings we have a generalisation of Osgood's theorem and for set-valued mappings we have an extension of Fort's theorem and a generalisation of Michael's selection theorem producing a densely defined selection with a natural continuity property relative to the domain. |
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Keywords: | 54C10 54C65 |
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