Definition of Nonempty. Meaning of Nonempty. Synonyms of Nonempty

- 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...
- 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...
- 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...
- 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...
- Cantor set. Every decreasing nested sequence of nonempty closed subsets S1 ⊇ S2 ⊇ ... in (X, d) has a nonempty intersection. Every increasing nested sequence...
- Every nonempty Baire space is nonmeagre. In particular, by the Baire category theorem every nonempty complete metric space and every nonempty locally...
- {\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...
- set of nonempty sets has a choice function. A weaker form of AC, the axiom of countable choice (ACω) states that every countable set of nonempty sets has...
- has a unique nonempty compact (closed and bounded) fixed set S. One way of constructing a fixed set is to start with an initial nonempty closed and bounded...