Ad
related to: subset of 36 9 or 7 wire to make 10
Search results
Results From The WOW.Com Content Network
A set A of natural numbers is an IP set if there exists an infinite set D such that FS(D) is a subset of A. Equivalently, one may require that A contains all finite sums FS((n i)) of a sequence (n i). Some authors give a slightly different definition of IP sets: They require that FS(D) equal A instead of just being a subset.
For instance, had been declared as a subset of , with the sets and not necessarily related to each other in any way, then would likely mean instead of . If it is needed then unless indicated otherwise, it should be assumed that X {\displaystyle X} denotes the universe set , which means that all sets that are used in the formula are subsets of X ...
In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment).
A collection of subsets of a topological space is called σ-locally finite [6] [7] or countably locally finite [8] if it is a countable union of locally finite collections. The σ-locally finite notion is a key ingredient in the Nagata–Smirnov metrization theorem , which states that a topological space is metrizable if and only if it is ...
(Proposition (9.9.4)) One important role that these constructibility results have is that in most cases assuming the morphisms in questions are also flat it follows that the properties in question in fact hold in an open subset. A substantial number of such results is included in EGA IV § 12. [11]
A bijection between two topological spaces is a homeomorphism if and only if the derived set of the image (in the second space) of any subset of the first space is the image of the derived set of that subset. [7] A space is a T 1 space if every subset consisting of a single point is closed. [8]
The first condition states that the whole set B, which contains all the elements of every subset, must belong to the nested set collection. Some authors [ 1 ] do not assume that B is nonempty. The second condition states that the intersection of every couple of sets in the nested set collection is not the empty set only if one set is a subset ...
In recursion theory, the mathematical theory of computability, a maximal set is a coinfinite recursively enumerable subset A of the natural numbers such that for every further recursively enumerable subset B of the natural numbers, either B is cofinite or B is a finite variant of A or B is not a superset of A.