A metric(adsbygoogle = window.adsbygoogle || []).push({}); don the topological space_{p}X×Y, withd(x,y) and_{X}d(x_{Y}_{1},y_{1}) being metrics onXandYrespectively, is defined as

d((x,y),(x_{p}_{1},y_{1}))=((d(x,y))_{X}^{p}+(d(x_{Y}_{1},y_{1}))^{p})^{1/p}

What does eachd((x,y),(x_{p}_{1},y_{1})) mean (geometrically or visually)?

as p[tex]\rightarrow[/tex][tex]\infty[/tex],

d=max((_{[tex]\infty[/tex]}d(x,y),_{X}d(x_{Y}_{1},y_{1})).

What is the meaning of "max(A,B)"?

Each of thed((x,y),(x_{p}_{1},y_{1})) are strongly equivalent; what does this mean geometically?

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# Topological space metrics

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