On Tychonoff's type theorem via grills
نویسنده
چکیده مقاله:
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 of Tychonoff. We shall also observe> that the above result is also equivalent to the Axiom of Choice.
منابع مشابه
on tychonoff's type theorem via grills
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...
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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...
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عنوان ژورنال
دوره 42 شماره 1
صفحات 37- 41
تاریخ انتشار 2016-02-01
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