Geodesic
A Necessary and Sufficient Condition for the Equivalence of the Topologies of Uniform and Compact Convergence
Canadian mathematical bulletin, Tome 22 (1979) no. 4, pp. 467-470

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Let (X, p) and (Y, d) be metric spaces with at least two points. It is usual for introductory courses in topology to study the set Yx of all functions mapping X to Y with the pointwise, compact-open, uniform convergence, and uniform convergence on compacta topologies. Some care is taken to show sufficient conditions for these topologies to be equivalent [1, 2]. However, the question of necessary conditions are dismissed with examples showing that the topologies are not in general equivalent. 
Clapp, Michael H.; Shiflett, Ray C. A Necessary and Sufficient Condition for the Equivalence of the Topologies of Uniform and Compact Convergence. Canadian mathematical bulletin, Tome 22 (1979) no. 4, pp. 467-470. doi: 10.4153/CMB-1979-060-9
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     title = {A {Necessary} and {Sufficient} {Condition} for the {Equivalence} of the {Topologies} of {Uniform} and {Compact} {Convergence}},
     journal = {Canadian mathematical bulletin},
     pages = {467--470},
     year = {1979},
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     doi = {10.4153/CMB-1979-060-9},
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