This article is not about the indecomposability attributed to the real line by constructive mathematics. See Indecomposability (constructive mathematics).
The first four stages of the construction of the bucket handle as the limit of a series of nested intersections
In point-set topology, an indecomposable continuum is a continuum that is indecomposable, i.e. that cannot be expressed as the union of any two of its proper subcontinua. In 1910, L. E. J. Brouwer was the first to describe an indecomposable continuum.
Indecomposable continua have been used by topologists as a source of counterexamples. They also occur in dynamical systems.
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In point-set topology, an indecomposablecontinuum is a continuum that is indecomposable, i.e. that cannot be expressed as the union of any two of its...
mathematics: Indecomposable module, in algebra Indecomposable distribution, in probability Indecomposablecontinuum, in topology Indecomposability (intuitionistic...
(1910) of an indecomposablecontinuum, and in fact it is possible for the common boundary of the three sets to be an indecomposablecontinuum. The Lakes...
this product. It is an example of a protorus, a solenoid, and an indecomposablecontinuum. Because they are a dense subset of the real numbers, the dyadic...
composant of a point p in a continuum A is the union of all proper subcontinua of A that contain p. If a continuum is indecomposable, then its composants are...
emphasized. The Siegel disc is either unbounded or its boundary is an indecomposablecontinuum. Filled Julia set for f c ( z ) = z ∗ z + c {\displaystyle f_{c}(z)=z*z+c}...
by Borsuk and Mazurkiewicz in their paper Sur les rétractes absolus indécomposables, C.R.. Acad. Sci. Paris 199 (1934), 110-112). There is some disagreement...
uncountable cardinal that is a (weak or strong) limit indecomposable ordinal An indecomposable ordinal is a nonzero ordinal that is not the sum of two...
matter, space, time, money, or abstract mathematical objects such as the continuum. The origin of the idea in the Western tradition can be traced to the...
multiplication of ordinals). Similarly, one can consider additively indecomposable ordinals (meaning a nonzero ordinal that is not the sum of two strictly...
or ⊥ {\displaystyle \bot } . Also the real line may be taken to be indecomposable in this sense. Undecidability of disjunctions also affects the claims...
set in the reals cannot have a left inverse, as it would violate indecomposability, by giving a retraction of the real line to the set {0,1}. Williams...
Hilbert space. An infinite-dimensional Banach space is hereditarily indecomposable when no subspace of it can be isomorphic to the direct sum of two infinite-dimensional...
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