 
Summary: On the boundary connectedness of connected tiles
By JUN LUO 1
School of Mathematics and Computing Science, Zhongshan University,
Guanhzhou 510275, China
email: mcsluoj@zsu.edu.cn
SHIGEKI AKIYAMA 2
Department of Mathematics, Faculty of Science, Niigata University,
Niigata, Japan
email: akiyama@math.sc.niigatau.ac.jp
J ˜
ORG M. THUSWALDNER 3
Department of Mathematics and Statistics, Leoben University,
Leoben, Austria
email: joerg.thuswaldner@unileoben.ac.at
(Received 29 August 2002)
1. Introduction
In the present paper we want to dwell upon topological properties of
ordinary as well as graph directed iterated function systems. Let us first
give the basic definitions.
It is well known that for a family of contractions f 1 , . . . , f k on R d , there
