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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.

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
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