A topological lattice on the set of multifunctions
Let X be a Wilker space and M(X,Y) the set of continuous multifunctions from X to a topological space Y equipped with the compact-open topology. Assuming that M(X,Y) is equipped with the partial order ⊂ we prove that (M(X,Y),⊂) is a topological V-semilattice. We also prove that if X is a Wilker nor...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1989-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171289000815 |
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| Summary: | Let X be a Wilker space and M(X,Y) the set of continuous multifunctions
from X to a topological space Y equipped with the compact-open topology. Assuming
that M(X,Y) is equipped with the partial order ⊂ we prove that (M(X,Y),⊂)
is a
topological V-semilattice. We also prove that if X is a Wilker normal space and
U(X,Y) is the set of point-closed upper semi-continuous multifunctlons equipped with
the compact-open topology, then (U(X,Y),⊂) is a topological lattice. |
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| ISSN: | 0161-1712 1687-0425 |