Reproduktionstechnik

Berechnen Sie Daten rundum Ihre Schwangerschaft wie z.B. die ✓ Schwangerschaftswoche den ✓ Geburtstermin das ✓ Sternzeichen den ✓ Beginn des Mutterschutzes und vieles mehr.

Eintrag vom: 13.02.2013.

For an example of a complete but not compact space R R $\mathbb{R}$ suffices. Compactness implies completeness. To see that is easy. Take a Cauchy sequence. Since we are on a compact set it has a convergent subsequence. But a Cauchy sequence with a convergent subsequence must converge (this is a good exercise if you don't know ...

 

What is the difference between a complete metric space and a closed set? Can a set be closed but not complete?

 

Complete measure spaces are a fairly standard notion. The standard Lebesgue measure on the line is complete for example. Keep that example in mind...many of the complicated looking definitions you'll encounter are attempts to generalize that example.

 

$({\mathbb{R}}^{k} {d}_{2})$ are complete. If the latter is the case is it proper language to ask if the metric itself is complete on a space rather than asking if the metric space is compete? I realize this is probably a bit nit-picky but I like to pay close attention to wording to avoid confusion.

 

I do not know how to arrive at my result that every compact metric space is complete. Any help? Thanks in advance. general-topology analysis

 

As we known Banach spaces are normed vector spaces where Cauchy sequences converge. Can someone give me some examples of vector spaces with a defined norm which are not complete?

 

What is motivation behind the definition of a complete metric space? Intuitively a complete metric is complete if they are no points missing from it. How does the definition of completeness (in t...

 

For a space to be defined as complete do we need a sequence of some sort? i.e. Completeness cannot be defined without a sequence? Further this sequence needs to satisfy the closure property?

 

There's a notion of completeness of a metric space and a notion of completeness of a basis and they're not the same thing. Hilbert spaces are defined to be in particular complete metric spaces. Completeness of a basis means something different. It means what you said and another way of stating it is that the span of the given system is dense in the Hilbert space. So one is an intrinsic ...

 

I keep facing König's lemma "Every finitely branching infinite tree over N N $\mathbb{N}$ has infinite branch". Why it is not taken "obvious" but needs a careful proof? It seems somewhat obvious but I guess I overlook something.