On a Family of Functions Defined by the Boundary Operator
Wroński, Stanisław
Real Anal. Exchange, Tome 25 (1999) no. 1, p. 359-362 / Harvested from Project Euclid
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For a topological space $X$, let $M(X,R)$ denote the family of all functions $f\in R^{X}$ such that $f(Fr(A))\subseteq Fr(f(A)).$ Let $N(X,R)$ denote the family of all continuous functions $f\in R^{X}$ such that $card(f^{-1}(c))=1$ for each $c\in \Biggl( \inf\limits_{x\in X}f(x),\sup\limits_{x\in X}f(x)\Biggr) .$ We show that $M(X,R)=N(X,R)$ if $X$ is a connected and locally connected Hausdorff space.
Publié le : 1999-05-15
Classification:  connected space,  locally connected space,  boundary,  continuous function,  54C08,  54C30,  54C05 
@article{1231187609,
     author = {Wro\'nski, Stanis\l aw},
     title = {On a Family of Functions Defined by the Boundary Operator},
     journal = {Real Anal. Exchange},
     volume = {25},
     number = {1},
     year = {1999},
     pages = { 359-362},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1231187609}
}

Wroński, Stanisław. On a Family of Functions Defined by the Boundary Operator. Real Anal. Exchange, Tome 25 (1999) no. 1, pp.  359-362. http://gdmltest.u-ga.fr/item/1231187609/