On differentiability of Peano type functions
M. Morayne (1984)
Colloquium Mathematicae
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M. Morayne (1984)
Colloquium Mathematicae
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Michał Morayne (1987)
Colloquium Mathematicae
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J. Cichoń, A. Szymański, B. Węglorz (1987)
Colloquium Mathematicae
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Miklós Laczkovich, Ákos K. Matszangosz (2015)
Colloquium Mathematicae
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The classical Denjoy-Young-Saks theorem gives a relation, here termed the Denjoy property, between the Dini derivatives of an arbitrary one-variable function that holds almost everywhere. Concerning the possible generalizations to higher dimensions, A. S. Besicovitch proved the following: there exists a continuous function of two variables such that at each point of a set of positive measure there exist continuum many directions, in each of which one Dini derivative is infinite...
I. Gasparis (2002)
Studia Mathematica
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A family is constructed of cardinality equal to the continuum, whose members are totally incomparable hereditarily indecomposable Banach spaces.
J. Krasinkiewicz (1974)
Fundamenta Mathematicae
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Jerzy Krzempek (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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It is shown that a certain indecomposable chainable continuum is the domain of an exactly two-to-one continuous map. This answers a question of Jo W. Heath.
George W. Henderson (1971)
Colloquium Mathematicae
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J. J. Charatonik (1978)
Colloquium Mathematicae
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Alessandro Andretta (2018)
Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana
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We give an overview of the continuum hypothesis, of its impact on mathematics, and on the foundations of set theory.
Charles Perry (2001)
Visual Mathematics
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S. Drobot (1971)
Applicationes Mathematicae
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Charatonik, Janusz J. (2003)
International Journal of Mathematics and Mathematical Sciences
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J. H. V. Hunt (1971)
Colloquium Mathematicae
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Victor Jiménez López, Jaroslav Smítal (2001)
Fundamenta Mathematicae
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In 1992 Agronsky and Ceder proved that any finite collection of non-degenerate Peano continua in the unit square is an ω-limit set for a continuous map. We improve this result by showing that it is valid, with natural restrictions, for the triangular maps (x,y) ↦ (f(x),g(x,y)) of the square. For example, we show that a non-trivial Peano continuum C ⊂ I² is an orbit-enclosing ω-limit set of a triangular map if and only if it has a projection property. If C is a finite union of Peano continua...
J. Krasinkiewicz (1974)
Fundamenta Mathematicae
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James Davis, W. Ingram (1988)
Fundamenta Mathematicae
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Rogério Augusto dos Santos Fajardo (2012)
Studia Mathematica
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Assuming ⋄, we construct a connected compact topological space K such that for every closed L ⊂ K the Banach space C(L) has few operators, in the sense that every operator on C(L) is multiplication by a continuous function plus a weakly compact operator. In particular, C(K) is indecomposable and has continuum many non-isomorphic indecomposable quotients, and K does not contain a homeomorphic copy of βℕ. Moreover, assuming CH we construct a connected compact K where...
J. Grispolakis, E. D. Tymchatyn (1979)
Colloquium Mathematicae
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Davis, H.S., Stadtlander, D.P., Swingle, P.M. (1962)
Portugaliae mathematica
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