Hyperconvergences. (English) Zbl 1068.54010

Dolecki, Szymon; Mynard, Frédéric

Appl. Gen. Topol. 4, No. 2, 391-419 (2003).

In this interesting and extended paper, the authors investigate the new concept of hyperconvergence, the coarsest convergence for which the natural evaluation map, valued in Sierpinski space, is continuous. The survey encompasses material from a number of papers produced by the authors; in particular their paper [Topology Appl. 104, 67–99 (2000; Zbl 0953.54002)]; the second author’s papers [Appl. Gen. Topol. 2, 119–154 (2001; Zbl 1007.54008) and [Commentat. Math. Univ. Carol. 41, 143–153 (2000; Zbl 1037.54504)]. Of especial interest are characterizations of various reflective and coreflective properties in terms of the underlying convergence.

Reviewer: Peter J. Collins (Oxford)

MSC:

54B20	Hyperspaces in general topology
54A20	Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)

Keywords:

hyperconvergence; canonical evaluation; reflexion; coreflexion

Citations:

Zbl 0953.54002; Zbl 1007.54008; Zbl 1037.54504