Monotone decompositions of continua irreducible about a finite subset

Monotone Decompositions of «continua1

A 0-continuum (9„-continuum) is a compact, connected, metric space that is not separated into infinitely many (more than n) components by any subcontinuum. The following results are among those proved. The first generalizes earlier joint work with E. J. Vought for ^„-continua, and the second generalizes earlier work by Vought for 6,-continua. A 0-continuum X admits a monotone, upper semicontinu...

Decompositions of Continua over the Hyperbolic Plane

The following theorem is proved. THEOREM. Let X be a homogeneous continuum such that Hl(X) ^ 0. Ij'$/ is the collection of maximal terminal proper subcontinua of X, then (1) The collection ff is a monotone, continuous, terminal decomposition ofX, (2) The nondegenerate elements of%? are mutually homeomorphic, indecomposable, cell-like, terminal, homogeneous continua of the same dimension as X, (...

Eleven Annotated Problems About Continua

A cohesive finite element for quasi-continua

In this paper, a cohesive finite element method (FEM) is proposed for a quasi-continuum (QC), i.e. a continuum model that utilizes the information of underlying atomistic microstructures. Most cohesive laws used in conventional cohesive FEMs are based on either empirical or idealized constitutive models that do not accurately reflect the actual lattice structures. The cohesive quasi-continuum f...

Continua Which Are the Sum of a Finite Number of Indecomposable Continua

Swingle [7]1 has given the following definitions. (1) A continuum M is said to be the finished sum of the continua of a collection G if G* = M and no continuum of G is a subset of the sum of the others.2 (2) If » is a positive integer, the continuum M is said to be indecomposable under index » if If is the finished sum of « continua and is not the finished sum of »+1 continua. Swingle has shown...