A metric space X is complete if and only if every decreasing sequence of non-empty closed subsets of X, with diameters tending to 0, has a non-empty intersection: if F < sub > n </ sub > is closed and non-empty, for every n, and diam ( F < sub > n </ sub >) → 0, then there is a point x ∈ X common to all sets F < sub > n </ sub >.

In this sense one speaks of the diameter rather than a diameter, because all diameters of a circle have the same length, this being twice the radius.

The largest fragment produced the main crater with a depth of 22 m. Eight smaller craters with diameters ranging from 12 to 40 m and depths varying from 1 to 4 m are all within 1 kilometer of the main crater.

Salmonella is a genus of rod-shaped, Gram-negative, non-spore-forming, predominantly motile enterobacteria with diameters around 0. 7 to 1. 5 µm, lengths from 2 to 5 µm, and flagella that grade in all directions ( i. e., peritrichous ).

They all have similar diameters of between 20 and 30 km.

If you measure the circumferences of circles of steadily larger diameters and divide the former by the latter, all three geometries give the value π for small enough diameters but the ratio departs from π for larger diameters unless Ω = 1:

In 1998, NASA formally embraced the goal of finding and cataloging, by 2008, 90 % of all near-Earth objects ( NEOs ) with diameters of 1 km or larger that could represent a collision risk to Earth.

The historical alto instruments by Sax that did survive all have inner diameters that are those Sax described in his saxotromba patent.

Given that the modern instruments all have larger diameters, it now clearly is more a saxhorn than a saxotromba.

Western tanager used taller trees ( p < 0. 01 ) and trees with larger diameters significantly ( p < 0. 001 ) more than their availability in all silvicultural treatments analyzed.

Despite their name, not all linear induction motors produce linear motion, some linear induction motors are employed for generating rotations of large diameters where the use of a continuous primary would be very expensive.

To test whether a given sum of diameters can be achieved without knowing the individual cluster diameters, one may try all maximal pairs of target diameters that add up to at most the given sum, representing each pair of diameters as a 2-satisfiability instance and using a 2-satisfiability algorithm to determine whether that pair can be realized by a clustering.

Probably because they originated from the edge of a larger parent body rather than a core, E-types are all small, with only three ( 44 Nysa, 55 Pandora, 64 Angelina ) having diameters above 50 kilometres and no others above 25 kilometers ( the biggest three also orbit atypically far, c. 3 AU, from the Sun ).

Because all diameters are the same, the Reuleaux triangle is an answer to the question " Other than a circle, what shape can a manhole cover be made so that it cannot fall down through the hole?

For diameters smaller than ¼ inch, the diameter is indicated by an integer number defined in the standard, for all other diameters, the inch figure is given.

In geometry, an arbelos is a plane region bounded by a semicircle of diameter 1, connected to semicircles of diameters r and ( 1 − r ), all oriented the same way and sharing a common baseline.

The four main telescopes at OHP are all reflecting telescopes with primary mirrors of diameters 1. 93 m, 1. 52 m, 1. 20 m and 0. 80 m. The 1. 93 m telescope was built by Grubb-Parsons and installed at the site in 1958.

A subset S of a metric space X is totally bounded if and only if, given any positive real number E, there exists a finite cover of S by subsets of X whose diameters are all less than E. ( In other words, a " size " here is a positive real number, and a subset is of size E if its diameter is less than E .) Equivalently, S is totally bounded if and only if, given any E as before, there exist elements a < sub > 1 </ sub >, a < sub > 2 </ sub >, ..., a < sub > n </ sub > of < i > X < i /> such that S is contained in the union of the n open balls of radius E around the points a < sub > i </ sub >.

Aristarchus pointed out that the Moon and Sun have nearly equal apparent angular sizes and therefore their diameters must be in proportion to their distances from Earth, so that that the diameter of the Sun was between 18 and 20 times larger than the diameter of the Moon.

Most modern launchers are standardised on a diameter for light torpedoes ( deck mounted aboard ship ) or a diameter for heavy torpedoes ( underwater tubes ), although other sizes of torpedo tube have been used: see Torpedo classes and diameters.

For submicrometre particle sizes, capillaries with diameters in the range of 0. 1 to 1 micrometres develop pressures in the range of to for silicate liquids and in the range of to for a metal such as liquid cobalt.

American wire gauge ( AWG ), also known as the Brown & Sharpe wire gauge, is a standardized wire gauge system used since 1857 predominantly in the United States and Canada for the diameters of round, solid, nonferrous, electrically conducting wire .< ref >< abbr title =" American Society for Testing And Materials "> ASTM </ abbr > Standard B 258-02, Standard specification for standard nominal diameters and cross-sectional areas of AWG sizes of solid round wires used as electrical conductors, ASTM International, 2002 </ ref > The cross-sectional area of each gauge is an important factor for determining its current-carrying capacity.

The ratio of these diameters is 1: 92, and there are 40 gauge sizes from No. 36 to No. 0000, or 39 steps.

At its most numerous, the Fiesta line comprised approximately 64 different items, including Flower Vases in three sizes, Divided Plates, Water Tumblers, Carafes, Teapots in two sizes, Five Part Relish Trays, and large Chop Plates in fifteen-inch and thirteen-inch diameters.

The head castings and valve head sizes from 1969 to 1976 were different, notably in passages for air injection and spark plug diameters ( 1969-1974 18 mm, 1975 and up 14 mm ).

Rubber bands are made in different diameters, colors, sizes, and strengths.

Diversified tree structure includes multi-layered canopies and canopy gaps, high variance of tree heights and diameters, diversity of decaying classes and sizes of woody debris, and diversity of tree species.

Res-o-Pads can be challenging to size correctly because ( unlike standard saxophone pads which come in 0. 5 mm size steps ) they are only available in 1 / 32nds of an inch sizes which may not always correspond closely to key-cup diameters.

Different sizes of lead diameters are available to accommodate various preferences and pencil builds, as shown in the table below.

The tubes have standard sizes for different pressure ranges, with standard diameters up to 100 mm.

The following table includes the most common sizes ; nominal head tube diameters are assuming a 0. 1-0. 2 mm interference fit, which is what most head tube reaming cutters are designed to bore.

To facilitate maximum performance out of various air guns the leading match pellet manufacturers produce pellets with graduated " head sizes ", which means the pellets are offered with front diameters from up to.

To facilitate maximum performance out of various air guns the leading match pellet manufacturers produce pellets with graduated " head sizes ", which means the pellets are offered with front diameters from 4. 48 mm up to 4. 51 mm.

Johannes Hevelius produced a very precise table of star sizes measured telescopically, but now the measured diameters ranged from just over six seconds of arc for first magnitude down to just under 2 seconds for sixth magnitude.

Further increases in the sizes of the labia ( majora and minora ) occur when the woman is sexually aroused — in preparation for coitus — wherein the labia become engorged with blood and increase the labial diameters two-to-three times.

The Mini CD has various diameters ranging from ; they are sometimes used for CD singles, storing up to 24 minutes of audio or delivering device drivers.

The diameters are the longest chords of the circle.

Conversely, factors that favor plate columns are: presence of solids in feed, high liquid rates, large column diameters, complex columns, columns with wide feed composition variation, columns with a chemical reaction, absorption columns, columns limited by foundation weight tolerance, low liquid rate, large turn-down ratio and those processes subject to process surges.

If the pulleys are of differing diameters, a mechanical advantage is realized.

Axial flow pumps have small diameters, but give relatively modest pressure increases, and multiple compression stages are needed, but work well with low density fluids.

Centrifugal pumps are far more powerful for high density fluids, but require physically large diameters for low density fluids.

They are manufactured in standardized diameters, and varying lengths depending on required impulse.

Standard motor diameters are 18, 24, 29, 38, 54, 75, 98, and 150 millimeters.

Pipelines are generally high capacity lines and have diameters of either 1, 020 or 1, 220 millimeters.

" Clinkers are nodules ( diameters, 0. 2-1. 0 inch ) of a sintered material that is produced when a raw mixture of predetermined composition is heated to high temperature.

A step-index fiber is characterized by the core and cladding refractive indices n < sub > 1 </ sub > and n < sub > 2 </ sub > and the core and cladding radii a and b. Examples of standard core and cladding diameters 2a / 2b are 8 / 125, 50 / 125, 62. 5 / 125, 85 / 125, or 100 / 140 ( units of µm ).

Guns are similar to rotors, except that they generally operate at very high pressures of 40 to 130 lbf / in² ( 275 to 900 kPa ) and flows of 50 to 1200 US gal / min ( 3 to 76 L / s ), usually with nozzle diameters in the range of 0. 5 to 1. 9 inches ( 10 to 50 mm ).

The largest such formations, called giant molecular clouds, have typical densities of 100 particles per cm < sup > 3 </ sup >, diameters of, masses of up to 6 million solar masses, and an average interior temperature of 10 K. About half the total mass of the galactic ISM is found in molecular clouds < ref > and in the Milky Way there are an estimated 6, 000 molecular clouds, each with more than 100, 000 solar masses.

Those parameters are determined from the ratio of the inner ( d ) and outer ( D ) diameters and the dielectric constant ().

Sybert, 1998 points out that it remains unproven that aortic root diameters that are relatively large for body surface area but still well within normal limits imply a risk for progressive dilatation.

Currently, coast Douglas-fir trees or more in height and in diameter are common in old growth stands, and maximum heights of and diameters up to have been documented.

In this group, pipelines are usually short-a couple of hundred metres-and with small diameters.

Usually, the tire diameters on mountain unicycles are either 24 or, allowing the rider to more easily roll over obstacles such as roots and rocks.

Objects with diameters smaller than are called meteoroids ( or meteorites if they strike the ground ).

This method does not give an easy understanding if a twist rate is relatively slow or fast when bores of different diameters are compared.

They are lytic in nature and are among the smallest viruses, with diameters of about only 30 nanometers.

Rotor diameters are comparable to the wingspan of a Boeing 747 jet-liner.