51. CMB 2000 (vol 43 pp. 208)
 Matoušková, Eva

Extensions of Continuous and Lipschitz Functions
We show a result slightly more general than the following. Let $K$
be a compact Hausdorff space, $F$ a closed subset of $K$, and $d$ a
lower semicontinuous metric on $K$. Then each continuous function
$f$ on $F$ which is Lipschitz in $d$ admits a continuous extension on
$K$ which is Lipschitz in $d$. The extension has the same supremum
norm and the same Lipschitz constant.
As a corollary we get that a Banach space $X$ is reflexive if and only
if each bounded, weakly continuous and norm Lipschitz function
defined on a weakly closed subset of $X$ admits a weakly continuous,
norm Lipschitz extension defined on the entire space $X$.
Keywords:extension, continous, Lipschitz, Banach space Categories:54C20, 46B10 

52. CMB 1999 (vol 42 pp. 190)
 Gilmer, Patrick M.

Topological Quantum Field Theory and Strong Shift Equivalence
Given a TQFT in dimension $d+1,$ and an infinite cyclic covering of
a closed $(d+1)$dimensional manifold $M$, we define an invariant
taking values in a strong shift equivalence class of matrices. The
notion of strong shift equivalence originated in R.~Williams' work
in symbolic dynamics. The TuraevViro module associated to a TQFT
and an infinite cyclic covering is then given by the Jordan form of
this matrix away from zero. This invariant is also defined if the
boundary of $M$ has an $S^1$ factor and the infinite cyclic cover
of the boundary is standard. We define a variant of a TQFT
associated to a finite group $G$ which has been studied by Quinn.
In this way, we recover a link invariant due to D.~Silver and
S.~Williams. We also obtain a variation on the SilverWilliams
invariant, by using the TQFT associated to $G$ in its unmodified form.
Keywords:knot, link, TQFT, symbolic dynamics, shift equivalence Categories:57R99, 57M99, 54H20 

53. CMB 1999 (vol 42 pp. 13)
 Brendle, Jörg

Dow's Principle and $Q$Sets
A $Q$set is a set of reals every subset of which is a relative
$G_\delta$. We investigate the combinatorics of $Q$sets and
discuss a question of Miller and Zhou on the size $\qq$ of the smallest
set of reals which is not a $Q$set. We show in particular that various
natural lower bounds for $\qq$ are consistently strictly smaller than
$\qq$.
Keywords:$Q$set, cardinal invariants of the continuum, pseudointersection number, $\MA$($\sigma$centered), Dow's principle, almost disjoint family, almost disjointness principle, iterated forcing Categories:03E05, 03E35, 54A35 

54. CMB 1998 (vol 41 pp. 348)
 Tymchatyn, E. D.; Yang, ChangCheng

Characterizing continua by disconnection properties
We study Hausdorff continua in which every set of certain
cardinality contains a subset which disconnects the space. We show
that such continua are rimfinite. We give characterizations of
this class among metric continua. As an application of our
methods, we show that continua in which each countably infinite set
disconnects are generalized graphs. This extends a result of
Nadler for metric continua.
Keywords:disconnection properties, rimfinite continua, graphs Categories:54D05, 54F20, 54F50 

55. CMB 1998 (vol 41 pp. 245)
 Yang, Lecheng

The normality in products with a countably compact factor
It is known that the product $\omega_1 \times X$ of
$\omega_1$ with an $M_1$space may be nonnormal. In this paper we
prove that the product $\kappa \times X$ of an uncountable regular
cardinal $\kappa$ with a paracompact semistratifiable space is normal
if{f} it is countably paracompact. We also give a sufficient
condition under which the product of a normal space with a paracompact
space is normal, from which many theorems involving such a product
with a countably compact factor can be derived.
Categories:54B19, 54D15, 54D20 
