However, in the context of topology, sequences do not fully encode all information about a function between topological spaces.

However, the product topology is " correct " in that it makes the product space a categorical product of its factors, whereas the box topology is too fine ; this is the sense in which the product topology is " natural ".

However, present observations cannot exclude the possibilities that the universe has more dimensions and that its spacetime may have a multiply connected global topology, in analogy with the cylindrical or toroidal topologies of two-dimensional spaces.

However, the node does not have any idea of the actual network topology, nor does the node need it.

However, large-scale application is problematic because of the problem of matching the correct neural topology to the market being studied.

However, it does synchronize routing tables at start up as OSPF does, and sends specific updates only when topology changes occur.

However, when the deck transformation group is a topological group whose topology is not discrete, difficulties arise.

However, since continuity ( the basic notion of topology ) only deals with the local structure, it can be difficult to formally define the obvious global difference.

However, the weak topology can be finer than the product topology if neither X nor Y is locally compact.

However, because many important spaces encountered in topology are topological manifolds, simplicial complexes, or CW complexes, which are constructed by piecing together very simple patches, a theorem such as that of Mayer and Vietoris is potentially of broad and deep applicability.

However, for constant sheaves such as the sheaf of integers this does not work: the cohomology groups defined using the Zariski topology are badly behaved.

However, there can be non-trivial " propagation " ( or tunneling amplitudes ) from to through an intervening manifold with ; this reflects the topology of.

However, the falsity of an h-principle is also an interesting statement, intuitively this means the objects being studied have non-trivial geometry that cannot be reduced to topology.

However, it is up to system integrators how they organize their bus topology.

However, results in the ability of these isoforms to bind to the BAD and BAK proteins, as well as in the structural topology and electrostatic potential of the binding groove, suggest differences in antiapoptotic activity for the two isoforms

However, the initiation sequences are generally either AT-rich or exhibit bent or curved DNA topology.

However, a dcpo with the Scott topology is a Hausdorff space if and only if the order is trivial.

However, a dcpo equipped with the Scott topology need not be sober: The specialization order induced by the topology of a sober space makes that space into a dcpo, but the Scott topology derived from this order is finer than the original topology.

However, just as all the buildings have not fallen and flowed back to their original mud, so the values which wanted them and saw that they were built have not all disappeared.

However, despite the insight of many of his observations, his own conclusions are open to suspicion because of his failure to employ at all times the correct research methods.

However, his subject matter and basic themes have remained surprisingly consistent, and these, together with certain key poetic images, may be traced through all his work, including the new jazz experiments.

However, last night the tapes were not run at all during the evening hours and all we got on TV were a few snatches which Douglas Edwards and Huntley and Brinkley could squeeze into their programs.

However, it determined that neither this factor, nor `` the fact that all concerned in high executive posts in both companies acted honorably and fairly, each in the honest conviction that his actions were in the best interests of his own company and without any design to overreach anyone, including Du Pont's competitors '', outweighed the Government's claim for relief.

However, in this case as elsewhere it was necessary to arrive at a single standard to be applied to all situations, representing an averaging of conditions, and thus to fix particular points in time which would be considered the dividing points between daytime and nighttime conditions.

However, in all of Prokofieff's music, young or mature, we find his profile -- his `` signature '' -- his craftsman's attitude.

However, that is not all he has to do.

However, after you've seen all the historical piazzas and plazas, the places and forums, the churches and museums, the palaces and castles, and begin to feel at home in the capitals of Europe, you'll want to change your course and follow the by-roads at will, far from the market places.

However, all admitted that the `` hindsight '' was not altogether lost.

However, three of the managers did say that they would agree to attend the proposed meeting if all of the other managers decided to attend.

However, the positions of all parties and leaders were constantly shifting.

However, my principal objection in this sort of novel is to the hackneyed treatment of race-drivers, pilots, submariners, atomic researchers, and all the machine-masters of our age as brooding mystics or hysterical fatalists.

However, in 1816, Thomas lost all of his land in court cases because of faulty property titles.

However, i ' thar is also still an Islamic ideal to which all Muslims should strive to adhere at all times.

However, it would require all data transmission to send eight bits when seven could suffice.

However, while usually Greek festivals were celebrated at the full moon, all the feasts of Apollo were celebrated at the seventh day of the month, and the emphasis given to that day ( sibutu ) indicates a Babylonian origin.

Experiments have been conducted to attempt the synthesis of ununennium ( Uue ), which is likely to be the next member of the group, but they have all met with failure .< ref name =" link "> However, ununennium may not be an alkali metal due to relativistic effects, which are predicted to have a large influence on the chemical properties of superheavy elements.

However, with an international language with wide variations in its dialects, such as English, it would be impossible to represent the language in all its variations with a single phonetic alphabet.

However, only a very small percentage of all these people has remained in Angola, either for personal reasons ( intermarriage ) or as professionals ( e. g. medical doctors ).

However, Aaron's snake ate up all the other snakes ( Exodus 7: 9 ) proving his rod was victorious.

However, in general, the books only feature mental battles when there is some reason for mind-to-mind contact ( for example, Trump contact ) and magic or Trump is involved in all three of the above conflicts, so it is not clear whether Zelazny intended his characters to have such a power ; the combination of Brand's " living trump " powers and his high Psyche ( as presented in the roleplaying game ) would have guaranteed him victory over Corwin.

However, they are still not closely related to the other vultures, and their similarities are due to convergent evolution.

However, as recently as the 1930s, it was determined that the two groups are not that closely related at all and are merely the product of convergent evolution and adapted in a similar way to a similar ecological niche.

However, the spaces in which every convergent filter has a unique limit are precisely the Hausdorff spaces.

However, as recently as the 1930s, this was determined to be an example of convergent evolution by the strong selective forces encountered by unrelated birds sharing the same lifestyle at different times and in different habitat.

However, Indonesia and Malaysia largely unified their previously divergent orthographies in 1972, and they along with Brunei have set up a joint commission to develop common scientific and technical vocabulary and otherwise cooperate to keep their standards convergent.

However such interpretation is not required to be possible, because formal power series are not required to give a convergent series when a nonzero numeric value is substituted for x.

However, modern opinion considers the apparent similarities the result of convergent evolution, and based on a wealth of evidence splits the classically defined " Pelecaniformes " into several groups.

However, as already indicated by the distinctness of these two, their morphology seems to be a convergent adaptation.

However, others ( e. g. D. S. Jordan, H. Hannibal, E. Casier, C. DeMuizon, T. J. DeVries, D. Ward, and H. Cappetta ) cite convergent evolution as the reason for the dental similarity.

Here, the right hand side is clearly not convergent for any non-zero value of t. However, by truncating the series on the right to a finite number of terms, one may obtain a fairly good approximation to the value of for sufficiently small t. Substituting and noting that results in the asymptotic expansion given earlier in this article.

However, the phenomena of convergent evolution, parallel evolution, and evolutionary reversals ( collectively termed homoplasy ) add an unpleasant wrinkle to the problem of estimating phylogeny.

However, biogeography and the molecular data build a strong case for this similarity being a case of convergent evolution between birds that are close relatives but by far not as close as their appearance would suggest.

However, these similarities may not be inherited from a common ancestor, but result from either parallel or convergent evolution.

However, a few formerly poor countries, notably Japan, do appear to have converged with rich countries, and in the case of Japan actually exceeded other countries ' productivity, some theorize that this is what has caused Japan's poor growth recently – convergent growth rates are still expected, even after convergence has occurred ; leading to over-optimistic investment, and actual recession.

However, Matthews and Lassiter did not find the Wonderlic to be a successful measure of fluid and crystallized intelligence, and they stated that " the Wonderlic test scores did not clearly show convergent or divergent validity evidence across these two broad domains of cognitive ability.

However, if the hypothesis proposed by Peter Galton and Paul Sereno is correct -- namely, that prosauropods and true sauropods share a common ancestor rather than the former giving rise to the latter -- then commonalities shared by Riojasaurus and true sauropods are likely due to convergent evolution.