- In mathematics, the
empty set or void set is the
unique set
having no elements; its size or
cardinality (count of
elements in a set) is zero. Some axiomatic...
-
mathematical field of point-set topology, a
continuum (plural: "continua") is a
nonempty compact connected metric space, or, less frequently, a
compact connected...
-
every indexed family ( S i ) i ∈ I {\displaystyle (S_{i})_{i\in I}} of
nonempty sets,
there exists an
indexed set ( x i ) i ∈ I {\displaystyle (x_{i})_{i\in...
- R\cup S} ∪ {\displaystyle \cup } of increasing
nonempty chain ∪ {\displaystyle \cup } of increasing
nonempty chain Arbitrary unions (of at least 1 set) Arbitrary unions...
- {\displaystyle (\star )} on a
nonempty set H {\displaystyle H} is a
mapping from H × H {\displaystyle H\times H} to the
nonempty power set P ∗ ( H ) {\displaystyle...
-
every d + 1 {\displaystyle d+1} of
these sets is
nonempty, then the
whole collection has a
nonempty intersection; that is, ⋂ j = 1 n X j ≠ ∅ . {\displaystyle...
-
efforts to
extend Schauder's work.
Schauder fixed-point theorem: Let C be a
nonempty closed convex subset of a
Banach space V. If f : C → C is
continuous with...
-
space is a
topological space X that
contains no
nonempty dense-in-itself subset. Equivalently,
every nonempty subset A of X
contains a
point isolated in A...
- others), and complete, i.e.,
which "lacks gaps" in the
sense that
every nonempty subset with an
upper bound has a
least upper bound in the set. More symbolically:...
-
space X such that
every (
nonempty)
irreducible closed subset of X is the
closure of
exactly one
point of X: that is,
every nonempty irreducible closed subset...
