Real Analysis Exchange

Uniform Continuity of a Product of Real Functions

G. Beer and S. Naimpally

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Abstract

We produce necessary and sufficient conditions for the pointwise product of two uniformly continuous real-valued functions defined on a metric space to be uniformly continuous.

Article information

Source
Real Anal. Exchange, Volume 37, Number 1 (2011), 213-220.

Dates
First available in Project Euclid: 30 April 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1335806773

Mathematical Reviews number (MathSciNet)
MR3016861

Zentralblatt MATH identifier
1254.26004

Subjects
Primary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27} 54C05: Continuous maps
Secondary: 54C30: Real-valued functions [See also 26-XX] 54E35: Metric spaces, metrizability

Keywords
uniform continuity pointwise product of functions emphatic uniform continuity of a product of a function pair oscillation joint oscillation

Citation

Beer, G.; Naimpally, S. Uniform Continuity of a Product of Real Functions. Real Anal. Exchange 37 (2011), no. 1, 213--220. https://projecteuclid.org/euclid.rae/1335806773


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References

  • R. Bartle, The elements of real analysis, Wiley, New York, 1976.
  • G. Beer and S. Levi, Strong uniform continuity, J. Math. Anal. Appl. 350 (2009), 568-589.
  • A. Caserta, G. Di Maio, and L. Holá, Arzelà's theorem and strong uniform continuity on bornologies, J. Math. Anal. Appl. 371 (2010), 384-392.
  • E. Elyash, G. Laush, and N. Levine, On the product of two uniformly continuous functions on the line, Amer. Math. Monthly. 67 (1960), 265-267.
  • R. Engelking, General topology, Polish Scientific Publishers, Warsaw, 1977.
  • N. Levine and N. Saber, On the product of real valued uniformly continuous functions in metric spaces, Amer. Math. Monthly 72 (1965), 20-28.
  • S. Nadler, Pointwise products of real uniformly continuous functions, Sarajevo J. Math 1 (2005), 117-127.
  • S. Willard, General topology, Addison-Wesley, Reading, MA, 1970.