A Necessary and Sufficient Condition for the Equivalence of the Topologies of Uniform and Compact Convergence
1979 ◽
Vol 22
(4)
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pp. 467-470
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Keyword(s):
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.
2012 ◽
Vol Vol. 14 no. 2
(Graph Theory)
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2000 ◽
Vol 11
(03)
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pp. 515-524
1908 ◽
Vol 28
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pp. 249-258
1972 ◽
Vol 18
(2)
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pp. 129-136
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1981 ◽
Vol 91
(1-2)
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pp. 135-145
1966 ◽
Vol 62
(4)
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pp. 673-677
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2007 ◽
Vol 49
(3)
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pp. 431-447
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