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Open mapping theorems for capacities

Oleh Nykyforchyn, Michael Zarichnyi (2011)

Fundamenta Mathematicae

For the functor of upper semicontinuous capacities in the category of compact Hausdorff spaces and two of its subfunctors, we prove open mapping theorems. These are counterparts of the open mapping theorem for the probability measure functor proved by Ditor and Eifler.

Open maps between Knaster continua

Carl Eberhart, J. Fugate, Shannon Schumann (1999)

Fundamenta Mathematicae

We investigate the set of open maps from one Knaster continuum to another. A structure theorem for the semigroup of open induced maps on a Knaster continuum is obtained. Homeomorphisms which are not induced are constructed, and it is shown that the induced open maps are dense in the space of open maps between two Knaster continua. Results about the structure of the semigroup of open maps on a Knaster continuum are obtained and two questions about the structure are posed.

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