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.
The determinant of the metric in a space determines the properties of that space, such as its curvature and distance measurements. It helps define the geometry and structure of the space.
I am also dying to know geometrical interpretation of semi-metric space . If anyone have idea please do infrom me as well
One metric ton is equivalent to 1,000 kilograms. The volume of space occupied by one metric ton of materials will vary depending on the density of the substance. For example, one metric ton of lead will take up less space than one metric ton of feathers due to their different densities.
No.
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
A system of measurement based on ten is known as the metric system. In this system, units are based on powers of ten, making conversions between different units simple and straightforward. The metric system is widely used around the world for its ease of use and consistency.