We consider a real-valued function f defined on the set of infinite branches X of a countably branching pruned tree T. The function f is said to be a limsup function if there is a function $u \colon T \to \mathbb {R}$ such that $f(x) = \limsup _{t \to \infty } u(x_{0},\dots ,x_{t})$ for each $x \in X$ . We study a game characterization of limsup functions, as well as a novel game characterization of functions of Baire class 1.

Duparc introduced a two-player game for a function f between zero-dimensional Polish spaces in which Player II has a winning strategy iff f is of Baire class 1. We generalize this result by defining a game for an arbitrary function f : X → Y between arbitrary Polish spaces such that Player II has a winning strategy in this game iff f is of Baire class 1. Using the strategy of Player II, we reprove a result concerning first return recoverable functions.

Our goal is to evaluate the role of triggering effects on the star formation and early stellar evolution by presenting a statistically large sample of cloud and low-mass YSO data. We conducted large area surveys (ranging from 400 square-degree to 10800 square-degree) in optical, NIR and FIR. The distribution of the ISM and low-mass YSOs were surveyed. A relative excess was found statistically in the number of dense and cold core bearing clouds and low mass YSOs in the direction of the FIR loop shells indicating a possible excess in their formation.