Displaying similar documents to “A decomposition theorem for collections of universal subcontinua”

Componentwise and Cartesian decompositions of linear relations

S. Hassi, H. S. V. de Snoo, F. H. Szafraniec

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Let A be a, not necessarily closed, linear relation in a Hilbert space ℌ with a multivalued part mul A. An operator B in ℌ with ran B ⊥ mul A** is said to be an operator part of A when A = B +̂ ({0} × mul A), where the sum is componentwise (i.e. span of the graphs). This decomposition provides a counterpart and an extension for the notion of closability of (unbounded) operators to the setting of linear relations. Existence and uniqueness criteria for an operator part are established...

Shrinking of toroidal decomposition spaces

Daniel Kasprowski, Mark Powell (2014)

Fundamenta Mathematicae

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Given a sequence of oriented links L¹,L²,L³,... each of which has a distinguished, unknotted component, there is a decomposition space 𝓓 of S³ naturally associated to it, which is constructed as the components of the intersection of an infinite sequence of nested solid tori. The Bing and Whitehead continua are simple, well known examples. We give a necessary and sufficient criterion to determine whether 𝓓 is shrinkable, generalising previous work of F. Ancel and M. Starbird and others....

The generalized equations of Riccati and their applications to the theory of linear differential equations

T. Iwiński

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CONTENTSIntroduction.............................................................................................................................. 31. Definition of the Riccati equation of the n-th order....................................................... 62. Theorems on the existence of solutions of R equations. Relations between the solutions of linear differential equations and the solutions of the corresponding R equations..................................................................................................