IJPAM: Volume 80, No. 3 (2012)

ON A STONE-WEIERSTRASS TYPE THEOREM FOR $C(X)$

Liaqat Ali Khan$^1$, Asma Thabit Al-Hamidi$^2$
$^1$Department of Mathematics
King Abdulaziz University
Jeddah, SAUDI ARABIA
$^2$Department of Mathematics
King Abdulaziz University, Girls Section
Jeddah, SAUDI ARABIA


Abstract. We give a simple and short proof of a weaker form of the Stone-Weierstrass theorem for $C(X)$. We also discuss some of its consequences regarding the characterization of closed and maximal ideals in $C(X)$.

Received: June 4, 2012

AMS Subject Classification: 46J10, 46J20, 41A30

Key Words and Phrases: compact space, continuous functions, uniform topology, approximation, Stone-Weierstrass theorem, ideal

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 80
Issue: 3