We are happy to announce that we have confirmation from Theoretical Computer Science that they will certainly publish the proceedings of this conference. Look at this site for further details as they develop.

Venu G. Menon

Gopalan@uconnvm.uconn.edu

RDKCC@cunyvm.cuny.edu

Driving directions to the Stamford Camps of the University of Connecticut can be found at http://www.sp.uconn.edu/~wwwstmfd/Ucs/About_uconn/dtdirections.html

The Conference will be held at "Auditorium 2" on the second floor

Schedule

10:30-11:30am Martin Escardo, University of Edinburgh, "A point-free
construction of the patch topology".

11:30am-11:45am Tea

11:45am-12:15pm: Michael A. Bukatin, Brandeis University, "Measures on
Functional Domains".

12:15pm-12:45pm: Ralph Kopperman, City College of CUNY, "Polish spaces,
cocompactly quasimetrizable spaces, and maximal point spaces. Joint work
with K. Ciesielski, and R. Flagg.

Lunch, 12:45pm-2:15pm

2:15-2:45pm Martin Escardo, University of Edinburgh, "Semantic domains,
injective spaces and monads". Joint work with Bob Flagg.

2:45-3:15pm Bruce Burdick

3:15-3:30 Tea

3:30-4pm Yung Kong

4pm-5pm: Ernest Manes, University of Massachusetts, "Constructing
topological spaces for topological and Boolean categories: Determinism,
predicate transformers, monads, collection classes (C++), hylomorphisms
(Haskell), open questions galore and who knows what all else?

ABSTRACTS

Michael A. Bukatin, Brandeis University, bukatin@cs.brandeis.edu
http://www.cs.brandeis.edu/~bukatin/papers.html
Measures on Functional Domains
Abstract. The talk addresses issues of constructing measures on functional
domains in a functorial way. In particular, the construction based on the
understanding of functional domains as retracts of Cartesian products of
domains via our earlier subdomain construction shall be described.

Martin Escardo, University of Edinburgh, mhe@dcs.ed.ac.uk,
A point-free construction of the patch topology.
Abstract: For a Scott domain, the Lawson topology is a compact-Hausdorff
refinement of the Scott topology. In this talk I'll present the following
construction of the Lawson topology from the Scott topology. Let S be the
lattice of Scott open sets of a Scott domain D, and let L be the set of
finite-meet preserving Scott continuous closure operators on S with the
pointwise order. Then L is a lattice isomorphic to the Lawson topology of
D. I'll also discuss the functorial aspects of this construction.
More generally, this holds for D an FS-domain. Even more generally, the
finite-meet-preserving Scott continuous closure operators on the topology
of a stably compact space form a lattice isomorphic to the patch topology.
Although I know that the finite-meet-preserving Scott continuous closure
operators on the topology of any topological space always form a
refinement of the topology, I don't know a direct point-set construction
of this refinement.
I'll discuss some applications of this localic construction of the patch
topology to constructive semantics. Our main example will be the real
numbers under their natural order. It is well-known that for this example,
the Scott topology coincides with the topology of lower semi-continuity,
and that the Lawson topology coincides Euclidean topology.

Martin Escardo, University of Edinburgh, mhe@dcs.ed.ac.uk. Joint work with
Bob Flagg.
"Semantic domains, injective spaces and monads".
Abstract: Many categories of semantic domains can be considered from an
order-theoretic point of view and from a topological point of view via the
Scott topology. The topological point of view is particularly fruitful for
considerations of computability in classical spaces such as the Euclidean
real line. When one embeds topological spaces into domains, one requires
that the Scott continuous maps between the host domains fully capture the
continuous maps between the guest topological spaces. This property of the
host domains is known as injectivity. For example, the continuous Scott
domains are characterized as the injective spaces over dense subspace
embeddings (Dana Scott, 1980). From a third point of view, the continuous
Scott domains arise as the algebras of a monad (Wyler, 1985). The
topological characterization turns out to follow from the algebraic
characterization and general category theory (Escardo 1998). We
systematically consider monads that arise in computer science and topology,
obtaining new proofs and discovering new characterizations of semantic
domains and topological spaces by injectivity.

Ralph Kopperman, City College of CUNY, (RDKCC@cunyvm.cuny.edu). Joint work
with K. Ciesielski, and R. Flagg.
Polish spaces, cocompactly quasimetrizable spaces,
and maximal point spaces.
Abstract: Jimmie Lawson has conjectured that a topological space is the
maximal point space of a bounded $\omega$-continuous poset, if and only if
it is a Polish space. We show that this conjecture holds and give a
bitopological characterization of these spaces that indicates how the
bounded $\omega$-continuous poset is constructed.
The results show a satisfying relationship between the three concepts
stated in our title: a classical analytic (and set theoretic) notion, a
construct of asymmetric topology, and the existence of a structure which
allows computational approximation of the elements of a given topological
space.

Ernest Manes, University of Massachusetts, (mhe@dcs.ed.ac.uk)
Constructing topological spaces for topological and Boolean categories:
Determinism, predicate transformers, monads, collection classes (C++),
hylomorphisms (Haskell), open questions galore and who knows what all else?
Abstract: We introduce three constructions --the perfect-closed topology,
the binary intersection topology and the quasifilter topology-- as tools to
produce a comparison functor to topological spaces and continuous maps from
a broad class of topological categories. For {deterministic} Boolean
categories, the {diamond} and box predicate transformers of dynamic logic
respectively induce topologies where open sets have program-invariance
properties. If P {P_F} is the COVARIANT power set functor of all {finite}
subsets, we are surprised to report that Pµ2 is a monad with (P_F)µ2 a
submonad which is a Boolean collection monad. A nearness space is modeled
as a binary relation N from Pµ2 X to PX, namely AA N S if AA is near and if
for every A in AA, A intersects the closure of S. Two of the three construc
tions above produce the usual functor from Near to R0-spaces. Prerequisites
for the talk include elementary category theory (coproducts, pullbacks,
natural transformations) and some experience with topological categories.

By title
Cyrus F. Nourani, Project_METAAI@COmpuServe.com.
"HIFI Comouting and Fixpoints"
Abstract: New tree computing techniques and an algebraic computing theory
defining recursion tree amplification had been put forth by [Nourani 94].
The infinitary language category Lw1,B had been defined. A generic
language topology and a functor from Lw1,B to Set are defined for a
functorial model theory. The functorial model theory can define the formal
semantics for computation with Lw1,B. The computations are fixpoints on
both model defintion and the tree computing notions. A preliminary
recursive computing theory is defined on the categories defining recursion
tree amplification by fixpoints on algebraic theories. The Amplification
Principle, TAP, is put forth based on relating a minimal function set F to
a recursion theoretic gain concept, defining computing efficiency by gain
minimizations. A recursion theorem is stated in terms of HIFI principles.

Salvador Romaguera, U. Politecnica de Valencia (sromague@mat.upv.es)
Michel Schellekens National U. of Ireland, Cork (m.schellekens@cs.ucc.ie)
Norm-weightable Riesz Spaces and the Dual Complexity Space