Selection principles in topology: New directions


Marion Scheepers




Most mathematical theories start from humble beginnings where a mathematician while examining some mathematical object makes fundamental, but extit{ad hoc}, observations. When the significance of these observations are realized some organised study begins during which these are explored in detail for some central examples. In this second part of theory building some general themes of investigation are identified. Then, it seems, one enters a third phase in which several mathematicians join in developing the theory. Typically this third phase is marked with much innovation, rapid expansion and application to other areas of mathematics. This brief discussion of the area of extit{Selection principles in Topology} will be organized according to these three phases.