Analysis

Gelbaum, Bernard R.; Olmsted, John M. H.

doi:10.1007/978-1-4612-0993-5_2

Cited by 11 publications

(13 citation statements)

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“…As in the proof of the previous results (and with help of the basic examples appearing in [17]) we also obtain the following results on lineability/coneability. …”

Section: Some Pathologies In Subsets Of Differentiable Functionsmentioning

confidence: 85%

Moduleability, algebraic structures, and nonlinear properties

García-Pacheco

Pérez-Eslava

Seoane‐Sepúlveda

2010

Journal of Mathematical Analysis and Applications

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We show that some pathological phenomena occur more often than one could expect, existing large algebraic structures (infinite dimensional vector spaces, algebras, positive cones or infinitely generated modules) enjoying certain special properties. In particular we construct infinite dimensional vector spaces of non-integrable, measurable functions, completing some recent results shown in García-Pacheco et al. (2009) [13], García-Pacheco and Seoane-Sepúlveda (2006) [15], Muñoz-Fernández et al. (2008) [20]. We prove, as well, the existence of dense and not barrelled spaces of sequences every non-zero element of which has a finite number of zero coordinates (giving partial answers to a problem originally posed by R.M. Aron and V.I. Gurariy in 2003).

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“…As in the proof of the previous results (and with help of the basic examples appearing in [17]) we also obtain the following results on lineability/coneability. …”

Section: Some Pathologies In Subsets Of Differentiable Functionsmentioning

confidence: 85%

Moduleability, algebraic structures, and nonlinear properties

García-Pacheco

Pérez-Eslava

Seoane‐Sepúlveda

2010

Journal of Mathematical Analysis and Applications

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“…The book by Gelbaum & Olmsted [9] is a classical resource for using counterexamples in advanced calculus and mathematical analysis courses.…”

Section: Statement 5 a Function Y = F(x) Is Bounded On R If For Anymentioning

confidence: 99%

Experience with using counterexamples in an introductory calculus class

Klymchuk

2014

International Journal of Mathematical Education in Science and

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“…The set En consists of 2 n intervals of length 4 -~. We define E = ~ En and X = E x E. The 1-dimensional Hausdorff measure on X (denoted by u) coincides with n>0 the pro-duct of two copies of the Cantor measure on E (concerning Cantor measures, see, e.g., [3]). We have supp u = X; moreover, u satisfies (5) and the Carleson condition.…”

Section: CLmentioning

confidence: 99%