Hyperconvergences

Szymon Dolecki; Frédéric Mynard

doi:10.4995/agt.2003.2041

Authors

Szymon Dolecki Université de Bourgogne
Frédéric Mynard University of Mississippi

DOI:

https://doi.org/10.4995/agt.2003.2041

Abstract

The hyperconvergence (upper Kuratowski convergence) is the coarsest convergence on the set of closed subsets of a convergence space that makes the canonical evaluation continuous. Sundry reective and coreective properties of hyperconvergences are characterized in terms of the underlying convergence.

Downloads

Download data is not yet available.

Author Biographies

Szymon Dolecki, Université de Bourgogne

Departement de Mathematiques

Frédéric Mynard, University of Mississippi

Department of Mathematics

References

J. Adámek, H. Herrlich, and E. Strecker. Abstract and Concrete Categories. John Wiley and Sons, Inc., 1990.

B. Alleche and J. Calbrix. On the coincidence of the upper Kuratowski topology with the cocompact topology. Topology Appl., 93:207-218, 1999. http://dx.doi.org/10.1016/S0166-8641(97)00269-1

G. Birkhoff. Lattice Theory. A.M.S., 1967.

G. Bourdaud. Espaces d'Antoine et semi-espaces d'Antoine. Cahiers de Topologie et Géométrie Différentielle, 16:107-133, 1975.

G. Choquet. Convergences. Ann. Univ. Grenoble, 23:55-112, 1947-48.

B. J. Day and G. M. Kelly. On topological quotient maps preserved by pullbacks or products. Proc. Camb. Phil. Soc., 67:553-558, 1970. http://dx.doi.org/10.1017/S0305004100045850

S. Dolecki. Convergence-theoretic methods in quotient quest. Topology Appl., 73:1-21, 1996. http://dx.doi.org/10.1016/0166-8641(96)00067-3

S. Dolecki. Convergence-theoretic characterizations of compactness. Topology Appl., 125:393-417, 2002. http://dx.doi.org/10.1016/S0166-8641(01)00283-8

S. Dolecki, G. H. Greco, and A. Lechicki. Compactoid and compact filters. Pacific J. Math., 117:69-98, 1985. http://dx.doi.org/10.2140/pjm.1985.117.69

S. Dolecki, G. H. Greco, and A. Lechicki. When do the upper Kuratowski topology (homeomorphically, Scott topology) and the cocompact topology coincide? Trans. Amer. Math. Soc., 347:2869-2884, 1995. http://dx.doi.org/10.1090/S0002-9947-1995-1303118-7

S. Dolecki and F. Mynard. Convergence-theoretic mechanisms behind product theorems. Topology Appl., 104:67-99, 2000. http://dx.doi.org/10.1016/S0166-8641(99)00012-7

R. Engelking. Topology. Heldermann Verlag, 1989.

K. H. Hofmann and J. D. Lawson. The spectral theory of distributive continuous lattices. Trans. Amer. Math. Soc., 246:285-309, 1978. http://dx.doi.org/10.1090/S0002-9947-1978-0515540-7

F. Mynard. Coreectively modified duality. Rocky Mountain Mathematical Journal., to appear.

F. Mynard. First-countability, sequentiality and tightness of the upper Kuratowski convergence. Rocky Mountain Mathematical Journal., 33(4), Winter 2003, to appear.

F. Mynard. Strongly sequential spaces. Comment. Math. Univ. Carolinae, 41:143-153, 2000.

F. Mynard. Coreectively modi_ed continuous duality applied to classical product theorems. Appl. Gen. Topology, 2:119-154, 2002.

F. Schwarz. Powers and exponential objects in initially structured categories and application to categories of limits spaces. Quaest. Math., 6:227-254, 1983. http://dx.doi.org/10.1080/16073606.1983.9632302

D. Scott. Continuous lattices. In F. W. Lawvere, editor, Toposes, Algebraic Geometry and Logic. Springer-Verlag, 1972. Lecture Notes in Math. 274.