## On a generalization of absolute neighborhood retracts.(English)Zbl 1166.54008

The authors introduce and study two new classes of spaces: absolute multi-retracts (AMR) and absolute neighborhood multi-retracts (ANMR), which generalize the concepts of absolute retract (AR) and absolute neighborhood retract (ANR), respectively. They show, among other things, that an ANMR need be neither an ANR nor an approximate ANR in the sense of M. H. Clapp. In the final section they show by means of specialized homological techniques that fixed point theory can be extended to ANMRs. In particular, they prove some fixed point of Lefschetz type for admissible maps defined on ANMRs.

### MSC:

 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) 55M15 Absolute neighborhood retracts 47H10 Fixed-point theorems 54C60 Set-valued maps in general topology
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