directed set वाक्य
उदाहरण वाक्य
मोबाइल
- Directed sets are a generalization of nonempty totally ordered sets.
- In topology, directed sets are used to define analysis.
- Observe that the scale is by definition a directed set.
- Any directed set " A " may be made into a Cauchy space.
- The notion defined above is sometimes called an "'upward directed set " '.
- Nets generalize the notion of a sequence by requiring the index set simply be a directed set.
- Directed sets also give rise to direct limits in abstract algebra and ( more generally ) category theory.
- These are posets in which every upward-directed set is required to have a least upper bound.
- On the other hand, consider the directed set ( in fact : the chain ) of finite sets
- Some authors ( and this article ) assume that a directed set is directed upward, unless otherwise stated.
- As in the case of limits of sequences, least upper bounds of directed sets do not always exist.
- That is, all totally ordered sets are directed sets ( contrast lattices are directed sets both upward and downward.
- That is, all totally ordered sets are directed sets ( contrast lattices are directed sets both upward and downward.
- Also note that, by considering directed sets of two elements, such a function also has to be monotonic.
- Cofinal subsets are very important in the theory of directed sets and cofinal subnet is the appropriate generalization of subsequence .
- A "'downward directed set "'is defined analogously, meaning when every pair of elements is bounded below.
- A "'net "'is a function from a ( possibly uncountable ) directed set to a topological space.
- Now, as in the case of sequences, we are interested in the " limit " of a directed set.
- Every sequence is a net, taking " A " to be the directed set of natural numbers with the usual ordering.
- In the formalization of order theory, this is just the "'least upper bound "'of the directed set.
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