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| In [[mathematics]], particularly in [[functional analysis]], a '''Mackey space''' is a [[locally convex topological vector space]] ''X'' such that the [[topology]] of ''X'' coincides with the [[Mackey topology]] τ(''X'',''X′''), the [[finer topology|finest topology]] which still preserves the [[continuous dual]].
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| ==Examples==
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| Examples of Mackey spaces include:
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| * All [[bornological space]]s.
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| * All Hausdorff locally convex [[barrelled space|quasi-barrelled]] (and hence all Hausdorff locally convex [[barrelled space]]s and all Hausdorff locally convex reflexive spaces).
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| * All Hausdorff locally convex [[metrizable space]]s.
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| ==Properties==
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| * A locally convex space <math>X</math> with continuous dual <math>X'</math> is a Mackey space if and only if each convex and <math>\sigma(X', X)</math>-relatively compact subset of <math>X'</math> is equicontinuous.
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| * The [[Completion (metric space)|completion]] of a Mackey space is again a Mackey space.
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| * A separated quotient of a Mackey space is again a Mackey space.
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| * A Mackey space need not be separable, complete, quasi-barrelled, nor <math>\sigma</math>-quasi-barrelled.
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| == References ==
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| * {{cite book |last=Robertson |first=A.P. |coauthors= W.J. Robertson |title= Topological vector spaces |series=Cambridge Tracts in Mathematics |volume=53 |year=1964 |publisher= [[Cambridge University Press]] | page=81 }}
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| * {{cite book | author=H.H. Schaefer | title=Topological Vector Spaces | publisher=[[Springer-Verlag]] | series=[[Graduate Texts in Mathematics|GTM]] | volume=3 | date=1970 | isbn=0-387-05380-8 | pages=132–133 }}
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| * {{cite book | author=S.M. Khaleelulla | title=Counterexamples in Topological Vector Spaces | publisher=[[Springer-Verlag]] | series=[[Graduate Texts in Mathematics|GTM]] | volume=936 | date=1982 | isbn=978-3-540-11565-6 | pages=31, 41, 55-58 }}
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| {{Functional Analysis}}
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| [[Category:Topological vector spaces]]
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| {{mathanalysis-stub}}
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Oscar is what my spouse loves to contact me and I totally dig that title. My working day occupation is a librarian. Body developing is one of the issues I adore most. Years in the past we moved to Puerto Rico and my family enjoys it.
Stop by my homepage; healthy food delivery - just click the following internet page -