The assumptions of a metric space except for symmetry.
The assumptions of a metric space except for symmetry.
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.
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.
I am also dying to know geometrical interpretation of semi-metric space . If anyone have idea please do infrom me as well
No.
Matter is defined as that which has mass and occupies space. There are procedures to measure both. Even if you can't measure the mass of an object directly (such as a gas), you can still determine it's mass by measuring the space it occupies. Pressure is one way to measure the mass of gas by the amount of space it occupies.
I don't think there is any energy associated with empty space.
One metric ton of feathers will have a much larger volume than a ton of steel ingots.
1 metric ton = 1,000 kilograms How much volume (space) it occupies depends on what substance it is.
-- 1 cubic meter of space is 1,000 liters of space. -- 1 liter of water has 1 kilogram of mass. -- 1,000 liters of water has 1,000 kilograms of mass = 1 metric ton -- 1 metric ton of water fills 1 cubic meter of space. -- A substance with a specific gravity of 2.7 packs 2.7 times as much mass into the same space. -- 2.7 metric tons of it pack into 1 cubic meter of space. -- The number of cubic meters it occupies is (the number of metric tons)/2.7 . -- For ANY substance, the number of cubic meters it fills is (the # of metric tons)/(specific gravity) .
prove that every metric space is hausdorff and first countable
Red Bull Sound Space at KROQ - 2011 Metric 1-9 was released on: USA: 21 June 2012