In general topology, a subset A {\displaystyle A} of a topological space is said to be dense-in-itself or crowded if A {\displaystyle A} has no isolated...

is dense in X {\displaystyle X} if the smallest closed subset of X {\displaystyle X} containing A {\displaystyle A} is X {\displaystyle X} itself. The...

Look up density or dense in Wiktionary, the free dictionary. Density and dense usually refer to a measure of how much of some entity is within a fixed...

In mathematics, a partial order or total order < on a set X {\displaystyle X} is said to be dense if, for all x {\displaystyle x} and y {\displaystyle...

dense-in-itself. A set S {\displaystyle S} with S = S ′ {\displaystyle S=S'} is called a perfect set. Equivalently, a perfect set is a closed dense-in-itself...

In mathematics, a subset of a topological space is called nowhere dense or rare if its closure has empty interior. In a very loose sense, it is a set...

X has cardinality at least 2 ℵ 0 {\displaystyle 2^{\aleph _{0}}} . Dense-in-itself Finite intersection property Subspace topology Jech, Thomas (2003)...

typically be less dense than the surrounding region, and so will rise until it reaches air that is either warmer or less dense than itself. The converse will...

In mathematics, a scattered space is a topological space X that contains no nonempty dense-in-itself subset. Equivalently, every nonempty subset A of X...

the canonical example. A set with no isolated point is said to be dense-in-itself (every neighbourhood of a point contains other points of the set)....

must be single points. It is then easy to verify that A is closed, dense-in-itself, and totally disconnected, having the cardinality of the continuum...

requires it to take on a more dense form—in effect to be more concentrated, compressed, or converted into a denser material. In an implosion-type nuclear...

– making the network denser and non-hierarchical. Because there is no highest level within a heterarchy but the heterarchy itself, control is decentralized...

open set. Equivalently, a set is dense if its closure is the whole space. Dense-in-itself set A set is dense-in-itself if it has no isolated point. Density...

A jungle is land covered with dense forest and tangled vegetation, usually in tropical climates. Application of the term has varied greatly during the...

In mathematics – specifically, in operator theory – a densely defined operator or partially defined operator is a type of partially defined function....

energy density and pressure to the vacuum itself. Fully 70% of the matter density in the universe appears to be in the form of dark energy. Twenty-six percent...

set is nowhere dense in R {\displaystyle \mathbb {R} } and hence meagre in R . {\displaystyle \mathbb {R} .} But it is nonmeagre in itself, since it is...

on the same set. No nonempty dense-in-itself subset Let S be a nonempty subset of X. If S contains p, then p is isolated in S (since it is an isolated point...

be densely defined if its domain is dense in X. This also includes operators defined on the entire space X, since the whole space is dense in itself. The...

dense Gδ set in a Baire space is a Baire space. The result need not hold if the Gδ set is not dense. See the Examples section. Every comeagre set in a...

Let M = Z \ {−1} = (0,1), then M is connected, so M is dense on itself and has no gaps, in regards to <. If −1 is not the smallest or the largest element...

topological space that is itself finite or countably infinite is separable, for the whole space is a countable dense subset of itself. An important example...

torture and rape of women and children, and many indiscriminate attacks in densely populated areas. After the Russian withdrawal from areas north of Kyiv...

replace 1H in water molecules to form heavy water (2H2O), which is about 10.6% denser than normal water (so that ice made from it sinks in normal water)...

Ebony is a dense black/brown hardwood, coming from several species in the genus Diospyros, which also includes the persimmon tree. A few Diospyros species...

populous county in the state. Brooklyn, at 37,339.9 inhabitants per square mile (14,417.0/km2), is the second most densely populated county in the U.S. after...

population will grow to 6.5 million in 2033–34. The four most densely populated suburbs in Australia are located in Sydney with each having more than 13...

metres (33 ft) in length and thanks to its hollow stems, floats easily. This results in large clusters of stem amassing and create dense mats along the...

x^{**}=1} ) is called dense. Every element of the form x ∨ x ∗ {\displaystyle x\vee x^{*}} is dense. D(L), the set of all the dense elements in L is a filter...