The aim of this paper is to point out a property of topological spaces admitting a continuous bijection onto [0,1] expressed in the following theorem. Theorem. Let X be a topological space admitting a continuous bijection onto [0,1], and let f: X to R be a lower semicontinuous function with connected sub-levels. Then, f has a global minimum. We conclude observing that none of the assumptions of the above theorem can be removed.
A property of spaces admitting a continuous bijection onto [0,1]
CARFI', David
2003-01-01
Abstract
The aim of this paper is to point out a property of topological spaces admitting a continuous bijection onto [0,1] expressed in the following theorem. Theorem. Let X be a topological space admitting a continuous bijection onto [0,1], and let f: X to R be a lower semicontinuous function with connected sub-levels. Then, f has a global minimum. We conclude observing that none of the assumptions of the above theorem can be removed.File in questo prodotto:
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