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Line 97: The topology of pointwise convergence on {{mvar\|F}} is identical to the subspace topology that {{mvar\|F}} inherits from {{math\|''Y''<sup>''T''</sup>}} when {{math\|''Y''<sup>''T''</sup>}} is endowed with the usual [[product topology]]. If {{mvar\|X}} is a non-trivial [[Completely regular space\|completely regular]] Hausdorff topological space and {{math\|C(''X'')}} is the space of all real (or complex) valued continuous functions on {{mvar\|X}}, ~~the~~ the topology of pointwise convergence on {{math\|C(''X'')}} is [[Metrizable TVS\|metrizable]] if and only if {{mvar\|X}} is countable.{{sfn \| Jarchow \| 1981 \| pp=43-55}} == 𝒢-topologies on spaces of continuous linear maps ==

Topologies on spaces of linear maps: Difference between revisions