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

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.


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