Some open problems in metric continuum theory are discussed. They concern 1) generalized homogeneity, in particular monotone homogeneity of dendrites; 2) planability of curves; 3) means on continua; 4) contractibility of continua; and 5) selectibility of continua.

based on the notion of micro-structure in linear elasticity presented by mindlin, a newextended continuum mechanics (ecm) formulation is derived which can be utilized to model thematerial behavior at atomic scale. an attempt has been made to present a formulation capable ofproducing the molecular dynamics (md) simulation results with less computational effort. to thisend, some new kinematical v...

A generalized solenoid is an inverse limit space with bonding maps that are (regular) covering maps of closed compact manifolds. We study the embedding properties of solenoids in linear space and in foliations. A compact and connected topological space is called a continuum. A space X is homogeneous if for every x, y ∈ X there exists a homeomorphism h : X → X such that h(x) = y. The space is bi...

In this paper, we provide a characterization as to when a locally connected generalized continuum (a locally compact connected separable metric space) has a countable compactiication of a certain order type. We then prove that for any two locally connected generalized continua with maximal countable compactiications X and Y of the same order type there is a perfect surjection f : X ! Y. This pr...

Abstract We derive analytical solutions for the uniaxial extension problem relaxed micromorphic continuum and other generalized continua. These may help in identification of material parameters continua which are able to disclose size effects.