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Zbl 0857.54011
Borsík, Ján
Products of simply continuous and quasicontinuous functions. (English)
[J] Math. Slovaca 45, No.4, 445-452 (1995). ISSN 0139-9918; ISSN 1337-2211/e

For a topological space $X$ let $P({\cal Q}_X)$ denote the family of all functions that can be factored into a finite product of quasicontinuous functions, and let ${\cal H}_X$ denote the family of all cliquish functions such that the sets $f^{-1}((0,\infty))$ and $f^{-1}((-\infty,0))$ are the union of an open set and a nowhere dense set. (For more on quasicontinuous and cliquish functions see {\it T. Neubrunn} [Real Anal. Exch. 14, 259-306 (1989; Zbl 0679.26003)].) In this paper the equality ${\cal H}_X=P({\cal Q}_X)$ is proved under the assumption that $X$ is a $\text{T}_3$ second countable space. More precisely, every $f\in{\cal H}_X$ is the product of three quasicontinuous functions. This improves a result of the reviewer [Math. Slovaca 40, 401-405 (1990; Zbl 0755.26002)]. \par \{Remark: Recently {\it A. Maliszewski} [Real Anal. Exch. 21, 320-329 (1996; Zbl 0843.54019)] proved that every $h\in{\cal H}_{\bbfR}$ is the product of two quasicontinuous functions\}.
[T.Natkaniec (Bydgoszcz)]

MSC 2000:: *54C08 Generalizations of continuity
26A15 Continuity and related questions (one real variable)

Keywords: quasicontinuity; simple continuity; cliquishness; quasicontinuous functions; cliquish functions

Citations: Zbl 0843.54019; Zbl 0679.26003; Zbl 0755.26002

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