Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42120160201On Tychonoff's type theorem via grills3741738ENA.TalabeigiDepartment of Mathematics, Payam Noor University, Tehran, Iran.Journal Article20140520Let $\{X_{\alpha}:\alpha\in\Lambda\}$ be a collection of topological spaces, and $\mathcal {G}_{\alpha}$ be a grill on $X_{\alpha}$ for each $\alpha\in\Lambda$. We consider Tychonoff\rq{}s type Theorem for $X=\prod_{\alpha\in\Lambda}X_{\alpha}$ 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 of Tychonoff. We shall also observe> that the above result is also equivalent to the Axiom of Choice.http://bims.iranjournals.ir/article_738_3e4f14cd54c0259750fb23e3c2edef57.pdf