Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 29 Issue 1
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- Pages.81-87
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- 1992
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
INVARIANCE OF DOMAIN THEOREM FOR DEMICONTINUOUS MAPPINGS OF TYPE ( $S_+$ )
Abstract
Wellknown invariance of domain theorems are Brower's invariance of domain theorem for continuous mappings defined on a finite dimensional space and Schauder-Leray's invariance of domain theorem for the class of mappings I+C defined on a infinite dimensional Banach space with I the identity and C compact. The two classical invariance of domain theorems were proved by applying the homotopy invariance of Brower's degree and Leray-Schauder's degree respectively. Degree theory for some class of mappings is a useful tool for mapping theorems. And mapping theorems (or surjectivity theorems of mappings) are closely related with invariance of domain theorems for mappings. In[4, 5], Browder and Petryshyn constructed a multi-valued degree theory for A-proper mappings. From this degree Petryshyn [9] obtained some invariance of domain theorems for locally A-proper mappings. Recently Browder [6] has developed a degree theory for demicontinuous mapings of type (
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