- In mathematics, the
infimum (abbreviated inf; pl.: infima) of a
subset S {\displaystyle S} of a
partially ordered set P {\displaystyle P} is the greatest...
- In mathematics, the
concepts of
essential infimum and
essential supremum are
related to the
notions of
infimum and supremum, but
adapted to
measure theory...
-
fashion for a
function (see
limit of a function). For a set, they are the
infimum and
supremum of the set's
limit points, respectively. In general, when...
-
partially ordered set in
which all
subsets have both a
supremum (join) and an
infimum (meet). A
conditionally complete lattice satisfies at
least one of these...
-
unique supremum (also
called a
least upper bound or join) and a
unique infimum (also
called a
greatest lower bound or meet). An
example is
given by the...
- {\textstyle \bigvee S,} and similarly, the meet of S {\displaystyle S} is the
infimum (greatest
lower bound),
denoted ⋀ S . {\textstyle \bigwedge S.} In general...
-
limit infimum and
limit supremum of a set
sequence always exist and can be used to
determine convergence: the
limit exists if the
limit infimum and limit...
-
points of a
metric space relative to the
intrinsic metric is
defined as the
infimum of the
lengths of all
paths from the
first point to the second. A metric...
- any two
points x and y is the
infimum of
lengths of
paths between them.
Unlike in a
geodesic metric space, the
infimum does not have to be attained. An...
- (f\ominus b)(x)=\inf _{y\in B}[f(x+y)-b(y)]} ,
where "inf"
denotes the
infimum. In
other words the
erosion of a
point is the
minimum of the
points in...
