Fixed point theorems for partially outward mappings. (English) Zbl 1168.54331
Summary: We generalize some classical theorems related to dimension. We extend Brouwer’s fixed point theorem to a class of mappings whose images are not necessarily a subset of the domain. These results also generalize theorems of B.R. Halpern and G.M. Bergman. As applications, we prove some theorems for maps that pull absolute retracts outward into attached sphere collars. We note relationships to the relative Nielsen theory and show that certain of our applications can also be obtained using results of H. Schirmer.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 54C55 | Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) |
| 54F15 | Continua and generalizations |
| 54F45 | Dimension theory in general topology |
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