on tychonoff's type theorem via grills

نویسندگان

a. talabeigi

department of mathematics‎, ‎payam noor university‎, ‎tehran‎, iran.

چکیده

‎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.‎

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عنوان ژورنال:
bulletin of the iranian mathematical society

جلد ۴۲، شماره ۱، صفحات ۳۷-۴۱

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