Homotopically labile points of locally compact metric spaces
How sensitive is to changes in and/or ?
We investigate how the Lindelöf property of the function space is influenced by slight changes in and/or .
Hurewicz properties, non distinguishing convergence properties and sequence selection properties
Hyperspace of the approximate inverse limit
Hyperspace selections avoiding points
We deal with a hyperspace selection problem in the setting of connected spaces. We present two solutions of this problem illustrating the difference between selections for the nonempty closed sets, and those for the at most two-point sets. In the first case, we obtain a characterisation of compact orderable spaces. In the latter case --- that of selections for at most two-point sets, the same selection property is equivalent to the existence of a ternary relation on the space, known as a cyclic...
Hyperspaces of noncompact metric spaces