Sometimes it is useful to consider all functions with certain parameters as " parametric family ", i . e . as an indexed family of functions.
22.
This prevents processes in different IPC namespaces from using, for example, the SHM family of functions to establish a range of shared memory between the two processes.
23.
Jean Cerf showed that a 1-parameter family of functions between two Morse functions could be approximated by one that is Morse at all but finitely many degenerate times.
24.
The spawn ( ) family of functions declared in process . h can replace it in cases where the call to fork ( ) is followed directly by exec ( ).
25.
In the early 1980s, Feichtinger introduced modulation spaces, a family of function spacesdefined by the behavior of the short-time Fourier transform with respect to a test function from the Schwartz space.
26.
Estimates \ hat F of F are usually restricted to be member of a well-defined parametric family of functions, for example the family of linear functions characterized by an intercept and a slope.
27.
;Final topology : On a set " X " with respect to a family of functions into X, is the finest topology on " X " which makes those functions continuous.
28.
Any regularity property of the " ? i ", & thinsp; such as continuity, differentiability, that is preserved under finite sums will be preserved for the sum of any subcollection of this family of functions.
29.
As a next step, one could ask,'if you have a 1-parameter family of functions which start and end at Morse functions, can you assume the whole family is Morse ?'In general the answer is no.
30.
Two important special cases of the initial topology are the product topology, where the family of functions is the set of projections from the product to each factor, and the subspace topology, where the family consists of just one function, the inclusion map.
