| p8cyturf | Date: Friday, 2013-12-20, 2:36 PM | Message # 1 |
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Major
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| Complete metric space
In a very space along with the discrete metric, your only Cauchy sequences are the type of which <a href=http://www.sia.fr/images/uggboots.html>http://www.sia.fr/images/uggboots.html</a> are constant from certain point on. Hence any discrete metric space is done.
The rational numbers Q usually are not complete. <a href=http://www.sia.fr/images/airjordan5.html>http://www.sia.fr/images/airjordan5.html</a> As an illustration, the map
can be a homeomorphism in between the complete metric space R plus the incomplete space it is the unit circle within the Euclidean plane with the point (0,1) deleted. The latter space shouldn't be complete to be the nonCauchy sequence corresponding to t=n as n runs from the positive integers is mapped to some nonconvergent Cauchy sequence around the circle.
You can easlily define a topological <a href=http://www.sia.fr/images/nb.html>ニューバランス 1400</a>
<a href=http://www.sia.fr/images/airjordan5.html>エアジョーダン 5</a>
<a href=http://www.sia.fr/images/uggboots.html>アグ ブーツ</a> space to be metrically topologically complete whether it's homeomorphic towards complete metric space. A topological condition to do this property owner how the space be metrizable along with an absolute G, which can be, a G in almost every topological space in which it will be embedded.
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