compact-open topology


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compact-open topology

[¦käm‚pakt ¦ō·pən tə′päl·ə·jē]
(mathematics)
A topology on the space of all continuous functions from one topological space into another; a subbase for this topology is given by the sets W (K,U) = {ƒ:ƒ(K)⊂ U }, where K is compact and U is open.
References in periodicals archive ?
Let's recall the definitions: By O (X) we denote the algebra of holomorphic functions on X endowed with compact-open topology.
O'Meara, On paracompactness in function spaces with the compact-open topology, Proc.
0,1] the group of endpoint-preserving homeomorphisms of the closed unit interval, equipped with the compact-open topology.
n]), (X, x)) equipped with the compact-open topology and denoted it by [[pi].