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 ${X_{alpha}:alphainLambda}$ 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.
UR - http://bims.iranjournals.ir/article_738.html
L1 - http://bims.iranjournals.ir/article_738_3e4f14cd54c0259750fb23e3c2edef57.pdf
ER -