No.
Any closed bounded subset of a metric space is compact.
A compact metric space is not necessarily complete. Compactness only guarantees that every sequence in the space has a convergent subsequence, while completeness requires that every Cauchy sequence converges to a point in the space.
A metric on a set is complete if every Cauchy sequence in the corresponding metric space they form converges to a point of the set in question. The metric space itself is called a complete metric space. See related links for more information.
any interval subset of R is open and closed
The question doesn't make sense, or alternatively it is true by definition. A Hilbert Space is a complete inner product space - complete in the metric induced by the norm defined by the inner product over the space. In other words an inner product space is a vector space with an inner product defined on it. An inner product then defines a norm on the space, and every norm on a space induces a metric. A Hilbert Space is thus also a complete metric space, simply where the metric is induced by the inner product.
A. L. Le Maraic has written: 'The metric encyclopedia, \\' -- subject(s): Conversion tables, Metric system 'The complete metric system with the international system of units (SI)' -- subject(s): Conversion tables, Metric system, Weights and measures
Yes , see related link below .
Umm i think because when Darcy Martinez.made the metric system
To prove that a metric space ((X, d)) is a topological space, you need to show that the open sets defined by the metric (d) satisfy the axioms of a topology. Specifically, you can define the open sets as the collection of all unions of open balls (B(x, r) = {y \in X \mid d(x, y) < r}) for all (x \in X) and (r > 0). Then, verify that this collection includes the empty set and the whole space (X), is closed under arbitrary unions, and is closed under finite intersections. If these conditions hold, then the metric space indeed induces a topology.
Here is a complete list of imperial/metric conversions (i.e. feet to meters): http://www.thetipsbank.com/convert.htm
metric to metric ?Multiply by 1.
Yes. Mexico is the 6th largest producer of blueberries in the world, with an annual production of 7,191 Metric Tons for 2012.