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Let X be a topological space, and let a subset be negligible if it is of first category, that is, if it is a countable union of nowhere-dense sets (where a set is nowhere-dense if it is not dense in any open set). Then the negligible sets form a sigma-ideal. Let X be a directed set, and let a subset of X be negligible if it has an upper bound ...
A nowhere dense set is not necessarily negligible in every sense. For example, if X {\displaystyle X} is the unit interval [ 0 , 1 ] , {\displaystyle [0,1],} not only is it possible to have a dense set of Lebesgue measure zero (such as the set of rationals), but it is also possible to have a nowhere dense set with positive measure.
In the mathematical field of general topology, a meagre set (also called a meager set or a set of first category) is a subset of a topological space that is small or negligible in a precise sense detailed below. A set that is not meagre is called nonmeagre, or of the second category. See below for definitions of other related terms.
What's the deal with Walmart's "Wirkin" Bag? Dubbed the "Birkin for the wirkin' class," Walmart has been in the news for carrying a viral dupe to the iconic Hermès bag that's become a symbol of ...
(Coincidentally, since a generating set always exists, e.g. M itself, this shows that a module is a quotient of a free module, a useful fact.) A generating set of a module is said to be minimal if no proper subset of the set generates the module. If R is a field, then a minimal generating set is the same thing as a basis.
The Cantor set is a meagre set (or a set of first category) as a subset of [0,1] (although not as a subset of itself, since it is a Baire space). The Cantor set thus demonstrates that notions of "size" in terms of cardinality, measure, and (Baire) category need not coincide.
5. Borden American Cheese Singles. The truth is, so many of these cheeses taste identical. Borden and Harris Teeter are really similar, both lacking any distinct flavors that make them unique or ...
The red subset = {1,2,3,4} has two maximal elements, viz. 3 and 4, and one minimal element, viz. 1, which is also its least element. In mathematics , especially in order theory , a maximal element of a subset S {\displaystyle S} of some preordered set is an element of S {\displaystyle S} that is not smaller than any other element in S ...