on tychonoff's type theorem via grills
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abstract
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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full texton tychonoff's type theorem via grills
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Journal title:
bulletin of the iranian mathematical societyPublisher: iranian mathematical society (ims)
ISSN 1017-060X
volume 42
issue 1 2016
Keywords
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