Large inductive dimension of the Smirnov remainder

The purpose of this paper is to investigate the large inductive dimension of the remainder of the Smirnov compactification of the n-dimensional Euclidean space with the usual metric, and give an application of it.Comment: 8 pages, accepted for publication in Houston Journal of Mathematic

The construction of P-expansive maps of regular continua: A geometric approach

AbstractIn this paper, we prove the following: Let G be a graph, f:G→G a continuous map and P a finite subset of G such that f(P)⊂P. Then there exist a regular continuum Z, a continuous map g:Z→Z and a semi-conjugacy π:G→Z such that(1) g is π(P)-expansive, and(2) if p,q∈P and Q is a subset of P with A∩Q≠∅ for any arc A in G between p and q, then A′∩π(Q)≠∅ for any arc A′ in Z between π(p) and π(q).In addition, f is point-wise P-expansive if and only if π|P is one-to-one.In this paper we are especially interested in the geometrical structure of Z. Actually we can see the complicated construction of Z