Statistics and Probability Commons^™

Openness And Monotoneity Of Induced Mappings, W. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

It is shown that for locally connected continuum X if the induced mapping C(f) : C(X) ->C(Y) is open, then f is monotone. As a corollary it follows that if the continuum X is hereditarily locally connected and C(f) is open, then f is a homeomorphism. An example is given to show that local connectedness is essential in the result.