TY - JOUR ID - 738 TI - On Tychonoff's type theorem via grills JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Talabeigi, A. AD - Department of Mathematics‎, ‎Payam Noor University‎, ‎Tehran‎, Iran. Y1 - 2016 PY - 2016 VL - 42 IS - 1 SP - 37 EP - 41 KW - Tychonoff's theorem KW - grills KW - Axiom of Choice DO - N2 - ‎Let $\{X_{\alpha}:\alpha\in\Lambda\}$ 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.‎ UR - http://bims.iranjournals.ir/article_738.html L1 - http://bims.iranjournals.ir/article_738_3e4f14cd54c0259750fb23e3c2edef57.pdf ER -