Let X be a complete metric space. Suppone k is a cloned and bounded subat with the pooperty that it containa a intinite set f pointo {xnŚ with the property that countukly d(xm, Xnl 7 2a 70 for all n#m. Show that Htheset k is not compact.

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Let X bu a complete metria space. Supp k is a cloned and
bounded subast with the property that it containa a countatly
intinite set f pointo {xnŚ with the property that
d(xm, Xnl 7 2a 70 for all n#m.
Show that theset k is not compact.
Transcribed Image Text:Let X bu a complete metria space. Supp k is a cloned and bounded subast with the property that it containa a countatly intinite set f pointo {xnŚ with the property that d(xm, Xnl 7 2a 70 for all n#m. Show that theset k is not compact.
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