- Y}
shows that any
prefilter (resp.
ultra prefilter,
filter subbase) on X {\displaystyle X} is also a
prefilter (resp.
ultra prefilter,
filter subbase)...
- filters/bases/subbases and uniformities.
Every filter is a
prefilter and both are
filter subbases.
Every prefilter and
filter subbase is
contained in a
unique smallest...
-
necessarily a
prefilter. The
ultra property can now be used to
define both
ultrafilters and
ultra prefilters: An
ultra prefilter is a
prefilter that is ultra...
- B-B\subseteq N.} A
prefilter B {\displaystyle {\mathcal {B}}} on an
additive topological group X {\displaystyle X}
called a
Cauchy prefilter if it satisfies...
- than) a
Cauchy prefilter is
necessarily also a
Cauchy prefilter and any
prefilter finer than a
Cauchy prefilter is also a
Cauchy prefilter. The
filter ****ociated...
- (respectively, a
Cauchy prefilter) F {\displaystyle F} on a
uniform space X {\displaystyle X} is a
filter (respectively, a
prefilter) F {\displaystyle F}...
- sets are
called prefilters, as well as the
aforementioned filter base/basis, and F is said to be
generated or
spanned by B. A
prefilter is
proper if and...
- In
control theory,
quantitative feedback theory (QFT),
developed by
Isaac Horowitz (Horowitz, 1963;
Horowitz and Sidi, 1972), is a
frequency domain technique...
- ({\mathcal {A}})} is a (proper)
prefilter. The
family A {\displaystyle {\mathcal {A}}} is a
subset of some (proper)
prefilter. The
upward closure π ( A )...
- f(x)} in Y . {\displaystyle Y.} Moreover, this
happens if and only if the
prefilter f ( N ( x ) ) {\displaystyle f({\mathcal {N}}(x))} is a
filter base for...
