In fact, the collection of all left cosets ( or right cosets ) of C in G is equal to the collection of all components of G. Therefore, the quotient topology induced by the quotient map from G to G / C is totally disconnected.

Therefore, more generally, a map projection is any method of " flattening " into a plane a continuous surface having curvature in all three spatial dimensions.

Therefore a map projection must have been used to create the map, and, conversely, maps could not exist without map projections.

Therefore, it would not be uncommon for 16th-century map to apply the label " China " just to the coastal region already well known to the Europeans ( e. g., just Guangdong on Abraham Ortelius ' 1570 map ), and to place the mysterious Cathay somewhere inland.

Therefore, it is possible to fully map the castle, and then utilize the map during subsequent games.

Therefore the bracket on A is just the Lie bracket of tangent vector fields and the anchor map is just the identity.

Therefore, if the sections never simultaneously vanish, they determine a form: ...: s < sub > r </ sub > which gives a map from X to P < sup > r </ sup >, and the pullback of the dual of the tautological bundle under this map is L. In this way, projective space acquires a universal property.

Therefore drivers will not notice any difference in signage, numbering, road standard or map marking from other national roads.

Therefore, MEG data is often combined with MR data into a composite image whereby functional information is overlaid on the corresponding anatomy to produce an activation map.

Therefore, viewing as a map between Hilbert spaces, we obtain its adjoint Φ < sup >*</ sup > given by

Therefore we can say a channel is a unital CP map between C *- algebras:

Therefore we now turn the map upside down, and then we have a true idea of our position, and not as the rest of the world wishes.

Therefore, in some chosen local coordinates, it is represented by the Jacobian of the corresponding smooth map from R < sup > m </ sup > to R < sup > n </ sup >.

Therefore, it is hoped that a major share of the overseas container traffic of Scandinavian and Baltic nations including the western part of Russia will be handled here ( map of feeder routes ).

Therefore the map is a multi-model.

Therefore the length of each parallel on the map is proportional to the cosine of the latitude, as it is on the globe.

Therefore, the induced map on spectra Spec ( B < sub > q < sub > 2 </ sub ></ sub >) → Spec ( A < sub > p < sub > 2 </ sub ></ sub >) is surjective and there exists a prime ideal of B < sub > q < sub > 2 </ sub ></ sub > that contracts to the prime ideal p < sub > 1 </ sub > A < sub > p < sub > 2 </ sub ></ sub > of A < sub > p < sub > 2 </ sub ></ sub >.

Therefore, he also points to the map of Vipsanius Agrippa.

Therefore, a pair of words whose earlier forms are distinct, yet similar, as far back as they have been traced, could in theory have come from a common root in an even earlier language, making them real cognates.

Therefore, it was more profitable for Attila to conclude peace and retreat back to his homeland.

Therefore, while some Kuwaitis originally trace themselves back to Arab origin ( specifically the Najd area or Iraq ), other Kuwaitis can trace themselves back to Iran and a few other non-Arab origins.

Therefore, looking at an image of oneself with the front / back axis flipped is the same as looking at an image with the left / right axis flipped and the whole figure rotated 180 degrees about the vertical axis, which is exactly what one sees when standing in front of a mirror.

In this approximately 800-word document about methods of franking letters he states, " Therefore, of Mr Hill ’ s plan of a uniform rate of postage … I conceive that the most simple and economical mode … would be by Slips … in the hope that Mr Hill ’ s plan may soon be carried into operation I would suggest that sheets of Stamped Slips should be prepared … then be rubbed over on the back with a strong solution of gum …".

Therefore, the size the track will determine where the 200-meter line is ( for 250 m tracks, it is about two-thirds of the way through the first bend ; for 200-meter tracks, it is the finish line ; for 400-meter tracks, it is the start line in the back straight ).

Therefore it must keep track of the running DC buildup, and always pick the code word that pushes the DC level back towards zero.

Therefore he gave it back to his enemy, Aeneas.

Therefore, despite the snow, the passengers were called back out to the plane just 15 minutes after leaving it.

Therefore if taken literally, they mean ‘ to walk straight back and forth .’ Although it can be translated loosely as meditative walking or walking meditation.

Therefore to this very day boats loaded with " Line Aquavit " set sail from Norway to Australia and back again before they are tapped on bottle and sold as part of the Norwegian Christmas traditions.

Therefore, although the government spends $ 1, it is likely that it receives back a significant proportion of the $ 1 in due course, making the net expenditure much less than $ 1.

Therefore, after 20 minutes of pursuit, Veneto was dropped back to 26, 000 meters ( 3, 000 more than the start ) and, as the visibility was worsened by smokescreen and bad weather, she ceased to fire at the British ships, it being impossible to observe the fall of the fire and with the enemy being faster than the Italian battleship.

Therefore, the entire back page of the News section is used for weather maps and temperature lists for the entire United States and many cities throughout the world, with data provided by Weather Channel meteorologists.

Therefore, the best practice was for a caravan to leave Hohhot in August, just after the grazing season ; upon reaching Gucheng, weaker camels could stay there until the next summer by grazing whatever vegetation is available in winter, while the stronger ones, after a few weeks of recovery on a grain diet ( grain being cheaper in Xinjiang than in eastern China ), would be sent back in late winter / early spring, taking along plenty of grain for fodder, and returning to Hohhot before the next grazing season.

Therefore, a signal intended to reflect back must be strong enough to cover at least twice the distance between the sender and the target — more in practice due to absorption losses.

Therefore, to maximise the rate of the S < sub > N </ sub > 2 reaction, the back of the substrate must be as unhindered as possible.

Therefore, in species that lack intra-mitochondrial PEP, oxaloacetate must be converted into malate or asparate, exported from the mitochondrion, and converted back into oxaloacetate in order to allow gluconeogenesis to continue.

Therefore Latvia was proclaimed a fully independent nation whose judicial foundation stemmed back to the statehood that existed before the occupation on June 17, 1940.

Therefore, they should be taken back ".

Therefore, daasoha in principle assumed that what belongs to God must return to Him and what came from society should be given back by way of selfless service.

Therefore, upon returning to Philadelphia, he made some tubes and brought them back to New York and showed them to the manager of the Roxbury Rubber Company.

Therefore, there is no certainty of success with a breeding back attempt and the results must be reviewed with caution.

Therefore, in recent years the club has risen from the depths of the Third Division to the heights of the First Division, then fallen back down to the basement league.