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• W2016542010 abstract "We use a technique involving skeletoids in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=sigma> <mml:semantics> <mml:mi>σ<!-- σ --></mml:mi> <mml:annotation encoding=application/x-tex>sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-compact metric <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=ARs> <mml:semantics> <mml:mtext>ARs</mml:mtext> <mml:annotation encoding=application/x-tex>text {ARs}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> to obtain some new examples of spaces homeomorphic to the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=sigma> <mml:semantics> <mml:mi>σ<!-- σ --></mml:mi> <mml:annotation encoding=application/x-tex>sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-compact linear spaces <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=l Subscript f Superscript 2> <mml:semantics> <mml:msubsup> <mml:mi>l</mml:mi> <mml:mi>f</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:annotation encoding=application/x-tex>l_f^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Sigma> <mml:semantics> <mml:mi mathvariant=normal>Σ<!-- Σ --></mml:mi> <mml:annotation encoding=application/x-tex>Sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. For example, we show that (1) every <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal alef 0> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi mathvariant=normal>ℵ<!-- ℵ --></mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>{aleph _0}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimensional metric linear space is homeomorphic to <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=l Subscript f Superscript 2> <mml:semantics> <mml:msubsup> <mml:mi>l</mml:mi> <mml:mi>f</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:annotation encoding=application/x-tex>l_f^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>; (2) every <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=sigma> <mml:semantics> <mml:mi>σ<!-- σ --></mml:mi> <mml:annotation encoding=application/x-tex>sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-compact metric linear space which is an <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=AR> <mml:semantics> <mml:mtext>AR</mml:mtext> <mml:annotation encoding=application/x-tex>text {AR}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and which contains an infinite-dimensional compact convex subset is homeomorphic to <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Sigma> <mml:semantics> <mml:mi mathvariant=normal>Σ<!-- Σ --></mml:mi> <mml:annotation encoding=application/x-tex>Sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula>; and (3) every weak product of a sequence of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=sigma> <mml:semantics> <mml:mi>σ<!-- σ --></mml:mi> <mml:annotation encoding=application/x-tex>sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-compact metric <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=ARs> <mml:semantics> <mml:mtext>ARs</mml:mtext> <mml:annotation encoding=application/x-tex>text {ARs}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> which contain Hilbert cubes is homeomorphic to <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Sigma> <mml:semantics> <mml:mi mathvariant=normal>Σ<!-- Σ --></mml:mi> <mml:annotation encoding=application/x-tex>Sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
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• W2016542010 title "Some applications of the topological characterizations of the sigma-compact spaces $lsp{2}sb{f}$ and $Sigma $" @default.
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• W2016542010 doi "https://doi.org/10.1090/s0002-9947-1984-0743748-7" @default.
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