Houston Problem Book Problem 25

From hyperspacewiki
Jump to: navigation, search

Problem 25 (HPB): Suppose $X$ is a tree-like continuum, its width $w(X)>0$, and $f$ is a continuous mapping from $X$ to a chainable continuum $Y$. Is it true that there exist, for each $a$ such that $0<a<w(X)$, two points $x$ and $y$ such that $d(x,y)=a$ and $f(x)=f(y)$? (Asked by A. Lelek, 9 February 1972)

Answer: Unknown