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- W2165451090 abstract "Suppose that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a Hausdorff space such that its Vietoris hyperspace <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis script upper F left-parenthesis upper X right-parenthesis comma tau Subscript upper V Baseline right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>F</mml:mi> </mml:mrow> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>τ<!-- τ --></mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>V</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>({mathcal {F}}(X),tau _{V})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has a continuous selection. Do disconnectedness-like properties of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> depend on the variety of continuous selections for <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis script upper F left-parenthesis upper X right-parenthesis comma tau Subscript upper V Baseline right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>F</mml:mi> </mml:mrow> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>τ<!-- τ --></mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>V</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>({mathcal {F}}(X),tau _{V})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and vice versa? In general, the answer is “yes” and, in some particular situations, we were also able to set proper characterizations." @default.
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- W2165451090 date "2001-02-09" @default.
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- W2165451090 title "Vietoris continuous selections and disconnectedness-like properties" @default.
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