• Thumbnail for Upper set
    In mathematics, an upper set (also called an upward closed set, an upset, or an isotone set in X) of a partially ordered set ( X , ≤ ) {\displaystyle...
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  • mathematics, particularly in order theory, an upper bound or majorant of a subset S of some preordered set (K, ≤) is an element of K that is greater than...
    6 KB (687 words) - 13:18, 26 September 2024
  • only if every upper set is also open (or equivalently every lower set is also closed). Let A be a subset of X. The smallest upper set containing A is...
    10 KB (1,414 words) - 18:14, 11 November 2024
  • a partially ordered set X has the least-upper-bound property if every non-empty subset of X with an upper bound has a least upper bound (supremum) in...
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  • Well-order (redirect from Well-ordered set)
    well-ordered set S contains for every subset T with an upper bound a least upper bound, namely the least element of the subset of all upper bounds of T...
    12 KB (1,882 words) - 17:26, 22 September 2024
  • than any other lower bound). Similarly, an upper bound of a subset S {\displaystyle S} of a partially ordered set ( P , ≤ ) {\displaystyle (P,\leq )} is an...
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  • definition. A directed set is a set A {\displaystyle A} with a preorder such that every finite subset of A {\displaystyle A} has an upper bound. In this definition...
    16 KB (2,731 words) - 18:28, 17 November 2024
  • non-empty totally ordered set with no upper bound. The integers form an initial non-empty totally ordered set with neither an upper nor a lower bound. The...
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  • Thumbnail for Partially ordered set
    order – Mathematical phrase Directed set – Mathematical ordering with upper bounds Graded poset – partially ordered set equipped with a rank functionPages...
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  • Natural density (redirect from Set density)
    A somewhat weaker notion of density is the upper Banach density d ∗ ( A ) {\displaystyle d^{*}(A)} of a set A ⊆ N . {\displaystyle A\subseteq \mathbb {N}...
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  • Thumbnail for Set (deity)
    Lower Egypt, and ruled the Nile Delta, from Avaris. They chose Set, originally Upper Egypt's chief god, the god of foreigners and the god they found...
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  • Thumbnail for Tall bike
    drive train is reconfigured to connect to the upper set of pedals, and the controls are moved to the upper handlebar area. Alternatively, a bicycle can...
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  • P is called Scott-open if it is an upper set and if it is inaccessible by directed joins, i.e. if all directed sets D with supremum in O have non-empty...
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  • {\displaystyle X} x ∈ X {\displaystyle x\in X} The upper contour set of x {\displaystyle x} is the set of all y {\displaystyle y} that are related to x...
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  • mathematics, a join-semilattice (or upper semilattice) is a partially ordered set that has a join (a least upper bound) for any nonempty finite subset...
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  • Thumbnail for Filter (mathematics)
    subset S of F is a base or basis for F if the upper set generated by S (i.e., the smallest upwards-closed set containing S) is equal to F. Since every filter...
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  • Thumbnail for Bounded set
    is called an upper bound of S. The terms bounded from below and lower bound are similarly defined. A set S is bounded if it has both upper and lower bounds...
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  • relation R is called well-founded (or wellfounded or foundational) on a set or, more generally, a class X if every non-empty subset S ⊆ X has a minimal...
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  • Thumbnail for Aero A.30
    related types, through the difference in spans between its wings – the upper set being of much greater span than the lower. In 1926, the Ministry of National...
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  • For a preordered set P, any upper set O is Alexandrov-open. Inversely, a topology is Alexandrov if any intersection of open sets is open. Algebraic...
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  • Thumbnail for Semi-continuity
    and upper semicontinuity and set-valued lower and upper semicontinuouty. An upper semicontinuous single-valued function is not necessarily upper semicontinuous...
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  • are the functors given with C. Their theory is a vast generalisation of upper sets in posets, and Yoneda's representability theorem generalizes Cayley's...
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  • Thumbnail for Preorder
    Preorder (redirect from Preordered set)
    has an upper bound. The definition of convergence via nets is important in topology, where preorders cannot be replaced by partially ordered sets without...
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  • preorder ≤ on a set X, there is a unique Alexandrov topology on X for which the specialization preorder is ≤. The open sets are just the upper sets with respect...
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  • terms of a pair of sets which give the lower and the upper approximation of the original set. In the standard version of rough set theory described in...
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  • Thumbnail for Monotonic function
    monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus...
    19 KB (2,467 words) - 04:06, 27 August 2024
  • Formally, the upper closure of a set S in a poset P is given by the set {x in P | there is some y in S with y ≤ x}. A set that is equal to its upper closure...
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  • dual concepts are upper and lower bounds, lower sets and upper sets, and ideals and filters. In topology, open sets and closed sets are dual concepts:...
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  • Thumbnail for Upper Deck Company
    The Upper Deck Company, LLC (colloquially as Upper Deck and Upper Deck Authenticated, Ltd. in the UK) is a private company primarily known for producing...
    57 KB (6,529 words) - 04:57, 15 November 2024
  • In mathematics, the upper topology on a partially ordered set X is the coarsest topology in which the closure of a singleton { a } {\displaystyle \{a\}}...
    2 KB (344 words) - 18:54, 17 November 2024