%0 Journal Article
%T On Tychonoff's type theorem via grills
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Talabeigi, A.
%D 2016
%\ 02/01/2016
%V 42
%N 1
%P 37-41
%! On Tychonoff's type theorem via grills
%K Tychonoff's theorem
%K grills
%K Axiom of Choice
%R
%X 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.
%U http://bims.iranjournals.ir/article_738_3e4f14cd54c0259750fb23e3c2edef57.pdf