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The embedding of a mapping space with compact open topology. (English) Zbl 0888.54014

Summary: We give an embedding theorem of a mapping space \(C_K(X,Y)\) with compact open topology in \(C_p({\mathcal C}(X),{\mathcal K}(Y))\) with pointwise convergence topology, where \({\mathcal K}(X)\), \({\mathcal K}(Y)\) are the hyperspaces of compact subsets with finite topology.

MSC:

54B20 Hyperspaces in general topology
54C35 Function spaces in general topology
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References:

[1] Engelking, R., General topology, (1989), Heldermann Berlin · Zbl 0684.54001
[2] Michael, E., Topologies on spaces of subsets, Trans. amer. math. soc., 71, 152-182, (1951) · Zbl 0043.37902
[3] Mizokami, T., Hyperspaces of a Moore space and a d-paracompact space, Glasnik mat., 30, 69-72, (1995) · Zbl 0856.54011
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