Zero divisors: continuous functions over R

  • Thread starter teleport
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  • #1
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Does the ring of continuous functions over the real numbers have no zero divisors? If no 0 divisor, how can I prove it? Else, what is a counter example?
 

Answers and Replies

  • #2
you should be able to define two nonzero continuous functions whose product is zero function...
 
  • #3
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Wow, yea probably. I want to find easy ones. Give me until tomorrow. I'm dead tired. Thanks
 
  • #4
Office_Shredder
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Keep in mind if a function is defined piecewise such that each piece is continuous, and all the endpoints match up, you've defined a new continuous function
 

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