let ${x_{alpha}:alphainlambda}$ be a collection of topological spaces, and $mathcal {g}_{alpha}$ be a grill on $x_{alpha}$ for each $alphainlambda$. we consider tychonoffrq{}s type theorem for $x=prod_{alphainlambda}x_{alpha}$ via the above grills and a natural grill on $x$ related to these grills, and present a simple proof to this theorem. this immediately yields the classical theorem...
