On singlevaluedness and continuity of monotone mappings
We shall prove that under CH every regular meta-Lindelöf -space which is locally has the -property. In addition, we shall prove that a regular submeta-Lindelöf -space is if it is locally and has locally extent at most . Moreover, these results can be extended from the class of locally -spaces to the wider class of -scattered spaces. Also, we shall give a direct proof (without using topological games) of the result shown by Peng [On spaces which are D, linearly D and transitively D, Topology...
Let be an open interval, a topological space and a metric space. Some local conditions implying continuity and quasicontinuity of almost all sections of a function are shown.