Porosity in spaces of Darboux-like functions. (English) Zbl 1035.26004

Rosen, Harvey

Real Anal. Exch. 26(2000-2001), No. 1, 195-200 (2001).

The author considers some sets of real functions of a real variable and spaces of functions endowed with the metric of uniform convergence. The main results: C is porous in Ext; AC is not porous in Conn; Conn is not porous in D, but Conn is a boundary set in D; D is porous in PC; where C(Ext, AC, Conn, D, PC) denotes a set (as well a space) of all continuous (extendable, almost continuous, connectivity, Darboux, perpherially continuous) functions.

Reviewer: Ryszard Pawlak (Łódź)

MSC:

26A15	Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
54C08	Weak and generalized continuity
54C35	Function spaces in general topology

Keywords:

extendable functions; peripherally continuous functions; connectivity functions; Darboux functions; porosity; metric of uniform convergence