The multicores in metric spaces and their application in fixed point theory. (English) Zbl 1253.55002

In the present paper the author defines notions of different types of so-called multicores and proves a result concerning the existence of fixed points for a certain class of multivalued maps (being admissible, compact and defined on a metric space). In fact it is shown that a multimap \(\varphi\) defined on a metric space \(X\) can be studied within the Lefschetz theory provided the closure of its image \(\varphi(X)\) is a multicore in an appropriate sense. There are no applications illustrating and justifying the presented approach for any concrete problem.


55M20 Fixed points and coincidences in algebraic topology
54H25 Fixed-point and coincidence theorems (topological aspects)
54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)
54C60 Set-valued maps in general topology
47H10 Fixed-point theorems
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