*Editors*: H. Amann (Zürich), G. Auchmuty (Houston), D. Bao (Houston),
H. Brezis (Paris), S. S. Chern (Berkeley), J. Damon (Chapel Hill), K. Davidson
(Waterloo), C. Hagopian (Sacramento), R. M. Hardt (Rice), J. Hausen (Houston),
J. A. Johnson (Houston), J. Nagata (Osaka), B. H. Neumann (Canberra), G. Pisier
(College Station and Paris), S. W. Semmes (Rice)
*Managing Editor*: K. Kaiser (Houston)

For the editorial board,

Charles Hagopian

Klaus Kaiser

*Contents*

**Harold R Bennett,
** Department of Mathematics, Texas Tech University, Lubbock, TX., U.S.A.
(graddir@math.ttu.edu),** Masami Hosobuchi**, Department of Housing and
Planning, Tokyo Kasei Gakuin University, Machida, Tokyo, JAPAN
(mhsbc@kasei-gakuin.ac.jp) and **David J. Lutzer, ** Department of
Mathematics, College of William and Mary, Williamsburg, VA., U.S.A.
(lutzer@math.wm.edu).

* Weakly Perfect Generalized Ordered Spaces,
* pp. 609-627.

ABSTRACT.
A space *X* is weakly perfect if each closed subset of *X* contains
a dense subset that is a G_{delta}-subset of *X.* This property
was introduced by Kocinac and later studied by Heath. We provide three
mechanisms for constructing ZFC examples of spaces that are weakly perfect but
not perfect. Some of our examples are compact linearly ordered spaces, while
others are types of Michael lines. Our constructions begin with special subsets
of the usual unit interval, e.g., perfectly meager subsets. We conclude by
giving a new and strictly internal topological characterization of perfectly
meager subsets of [0,1], namely that a topological space * X* is
homeomorphic to a perfectly meager subset of [0,1] if and only if
*X* is a zero-dimensional separable metrizable space with the property that
every subset * A* of *X *contains a countable set *B* that is
dense in *A *and is a G_{delta}-subset of *X.*

**L. Block,
** University of Florida (block@math.ufl.edu) , **J. Keesling, **
University of Florida (jek@math.ufl.edu) and **V.V. Uspenskij, ** Ohio
University (uspensk@math.ohiou.edu).

* Inverse Limits which are the Pseudoarc ,
* pp. 629-638.

ABSTRACT. Let C_{s(I,I)} denote the space of
surjective continuous maps of the compact interval * I * to itself with the
uniform topology. Given a map *f* in C_{s(I,I)}, let *(I,f) *
denote the inverse limit space obtained from the inverse sequence all of whose
maps are *f *and all of whose spaces are *I. * We show that the set of *
f *in C_{s(I,I)} such that *(I,f) * is homeomorphic to the
pseudoarc is nowhere dense in C_{s(I,I)}. Also, we show that if * f *
is any continuous map of * I * to itself such that * f * has a
periodic point of period two or larger, but
* f * has no periodic point of odd period larger than one, then *(I,f) *
is not homeomorphic to the pseudoarc. It follows that if * f * is any
continuous map of
*I * to itself with *(I,f) * the pseudoarc and with topological
entropy positive, then the topological entropy of
* f * is greater than log(2)/2.

**Janusz J. Charatonik,
** Mathematical Institute, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384
Wroclaw, Poland (jjc@hera.math.uni.wroc.pl).

* On generalized rigidity ,
* pp. 639-660.

ABSTRACT.
Concepts of chaotic and of rigid spaces with respect to a given class of
mappings are introduced and studied in the paper. A special attention is paid to
the classes of open and of monotone mappings. The obtained results are applied
to dendrites.

**Alex Clark, ** Department of Mathematics, University of North Texas,
Denton, TX 76203-1430 (alexc@unt.edu).

* Solenoidalization and Denjoids,
* pp. 661-692.

ABSTRACT. We describe a method (solenoidalization) of
obtaining flows on kappa --solenoids from a given flow on a kappa --torus. When
we apply this process to the Denjoy flows on **T**^{2} we obtain
flows whose minimal sets we call denjoids. We give a topological classification
of these indecomposable, one-dimensional continua.

**J. F. Davis
** and **Sam B. Nadler Jr., ** Department of Mathematics, West Virginia
University, P.O. Box 6310, Morgantown, WV 26506-6310 (nadler@math.wvu.edu).

* Hereditarily Weakly Confluent Mappings Onto S ^{1}
,
* pp. 693--720.

ABSTRACT. Results are obtained about the existence and behavior of hereditarily weakly confluent maps of continua onto the unit circle

**Valentin Gutev,
** School of Mathematical and Statistical Sciences, Faculty of Science,
University of Natal, King George V Avenue, Durban 4041, South Africa.

* An Exponential Mapping Over Set-Valued
Mappings,
* pp. 721-739.

ABSTRACT. The paper presents an approach to
``selection homotopy extension'' properties of set-valued mappings showing that
they become equivalent to usual selection extension properties of exponential
set-valued mappings associated to them. As a result, several ``controlled''
homotopy extension theorems are obtained like consequences of ordinary selection
theorems. Also, involving set-valued mappings, a simple proof of the Borsuk
homotopy extension theorem is given.

**K.T. Hallenbeck****,** Department of Mathematics, Widener
University, Chester, Pa 19013.

* Estimates of Spans of a Simple Closed
Curve Involving Mesh,
* pp. 741-745.

ABSTRACT. We show that the dual effectively monotone
span of a simple closed curve *X* in the plane does not exceed the infimum
of the set of positive numbers *m* such that a chain with mesh *m *
covers *X.* We also include a short direct proof of a known inequality
sigma_{0} (0) <= epsilon (X) where *X* is a continuum.

**David Handel,** Department of Mathematics, Wayne State University,
Detroit, Michigan 48202, USA (handel@math.wayne.edu).

* Some Homotopy Properties of Spaces of Finite
Subsets of Topological Spaces,
* pp. 747-764.

ABSTRACT. For X a non-empty topological space and k a
positive integer, we denote by Sub(X,k) the set of non-empty subsets of X having
cardinality less than or equal to k, suitably topologized. The Sub(- ,k) are
homotopy functors and their properties are studied. We prove that if X is
Hausdorff and path-connected, then for all integers k greater than or equal to
1, the inclusion maps from Sub(X,k) into Sub(X,2k+1) induce the trivial
homomorphisms in all homotopy groups. In the direction of non-triviality, we
prove that if X is a non-empty closed manifold of dimension at least 2, then for
each positive integer k, Sub(X,k) is homologically non-trivial.

**Morris W. Hirsch,
** Department of Mathematics, University of California, Berkeley, CA
94720-3840 (hirsch@math.berkeley.edu) .

* Topology of Fixed Point Sets of Surface
Homeomorphisms ,
* pp. 765-789.

ABSTRACT. This paper investigates the topology of the
fixed point set F of an orientation preserving homeomorphism of a connected
surface M, under the assumptions that M has finitely generated homology, F is
compact and nonempty with finitely many components, and no complementary
component of F is an open cell. This last condition holds if area is preserved,
or nonwandering points are dense, or there is a nowhere dense global attractor.
The main conclusion is that the Euler characteristic of F for Cech cohomology is
finite and no smaller than the Euler characteristic of M. Applications are made
to attractors, analytic homeomorphisms, homoclinic points, prime power iterates,
and commuting homeomorphisms.

**Tetsuya Hosaka, **Institute of Mathematics, University of Tsukuba,
Tsukuba, 305-8571, Japan, (thosaka@math.tsukuba.ac.jp), and **Katsuya Yokoi,**
Department of Mathematics, Interdisciplinary faculty of Science and Engineering,
Shimane University, Matsue, 690-8504, Japan (yokoi@math.shimane-u.ac.jp).

* The Boundary and the Virtual Cohomological
Dimension of Coxeter Groups,
* pp. 791-805.

ABSTRACT. This paper consists of three parts:

1) We give some properties about the *virtual cohomological dimension*
(*vcd*, for short) of Coxeter groups over principal ideal domains.

2) For a right-angled Coxeter group with *n-vcd* over a PID *R*,
we construct a sequence of parabolic subgroups with
*i-vcd* over *R* for *i* less than or equal to *n*.

3) We show that a parabolic subgroup of a right-angled Coxeter group is of
finite index if and only if their boundaries coincide.

**Ondrej F.K. Kalenda,
** Department of Math. Analysis, Faculty of Mathematics and Physics, Charles
University, Sokolovska 83, 186 75 Praha 8, Czech Republic}
(kalenda@karlin.mff.cuni.cz).

* On Double-Derived Sets in Topological
Spaces ,
* pp. 807-809.

ABSTRACT. We characterize topological spaces which
have a subset with non-closed double-derived set. As a corollary we obtain that
the double-derived set of an arbitrary subset of a T_{0} topological
space is closed. This answers in the negative a question asked by A.Lelek in
Houston Problem Book (1995).

**Takuo Miwa, ** Department of Mathematics, Shimane University, Matsue
690-8504, Japan (miwa@math.shimane-u.ac.jp).
* On Fibrewise Retraction and Extension ,
* pp. 811-831.

ABSTRACT. We study fibrewise retracts and extensions.
We introduce notions of absolute (nbd) retracts (or extensor) over a base space
B relative to a fibrewise class Q, and a notion of fibrewise adjunction spaces.
We study the relations of fibrewise ANR and ANE, and fibrewise contractibility
and fibrewise ANE.

**Robert Pierce, **Dr. Robert Pierce, 3260 Schneider Rd. #106, Toledo
Ohio 43614 (Bobscram@aol.com).

* Special Unions of Unicoherent Continua ,
* pp. 833-868.

ABSTRACT. It is proved that a Hausdorff continuum is
unicoherent if it is the union of two unicoherent continua whose intersection is
connected and locally connected.

**Elzbieta Pol **and **Roman Pol**, Institute of Mathematics,
University of Warzaw, Banacha 2, 02-097 Warzaw, Poland (pol@mimuw.edu.pl) .

* On the Krasinkiewicz - Minc Theorem concerning
Countable Fans ,
* pp. 869-876.

ABSTRACT. A strengthening of a remarkable theorem of
Krasinkiewicz and Minc is discussed to the effect that there are planar fans D_{alpha},
alpha < omega _{1}, such that if X is completely metrizable separable
and each D_{alpha} is a continuous (homeomorphic) image of a continuum
in X, then so is every chainable continuum. We shall also give an analogous
strengthening of a theorem of Mackowiak concerning hereditarily decomposable
chainable continua.

**Yun Ziqiu**, Department of Mathematics Suzhou University Suzhou, Jiangsu
People's Republic of China (yunziqiu@public1.sz.js.cn) and **Heikki J.K.
Junnila,** Department of Mathematics University of Helsinki Helsinki Finland
(heikki.junnila@helsinki.fi).

* On a Special Metric ,
* pp. 877-882.

ABSTRACT. In this note, we prove that whenever d is a
compatible metric for a sufficiently large hedgehog space J, there exist a
positive number r and a point x of the space J such that the family {B(y,r):
d(y,x)<r} contains uncountably many distinct sets. This result provides a
negative answer to a question raised by J. Nagata. We also give positive answers
to the same question under some extra conditions.