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Displaying 81 – 100 of 192

Multipliers of spaces of derivatives

Jan Mařík, Clifford E. Weil (2004)

Mathematica Bohemica

For subspaces, $X$ and $Y$ , of the space, $D$ , of all derivatives $M (X, Y)$ denotes the set of all $g \in D$ such that $f g \in Y$ for all $f \in X$ . Subspaces of $D$ are defined depending on a parameter $p \in [0, \infty]$ . In Section 6, $M (X, D)$ is determined for each of these subspaces and in Section 7, $M (X, Y)$ is found for $X$ and $Y$ any of these subspaces. In Section 3, $M (X, D)$ is determined for other spaces of functions on $[0, 1]$ related to continuity and higher order differentiation.

Normal numbers and subsets of N with given densities

Haseo Ki, Tom Linton (1994)

Fundamenta Mathematicae

For X ⊆ [0,1], let $D_{X}$ denote the collection of subsets of ℕ whose densities lie in X. Given the exact location of X in the Borel or difference hierarchy, we exhibit the exact location of $D_{X}$ . For α ≥ 3, X is properly $D_{ξ} (Π_{α}^{0})$ iff $D_{X}$ is properly $D_{ξ} (Π_{1 + α}^{0})$ . We also show that for every nonempty set X ⊆[0,1], $D_{X}$ is $Π_{3}^{0}$ -hard. For each nonempty $Π_{2}^{0}$ set X ⊆ [0,1], in particular for X = x, $D_{X}$ is $Π_{3}^{0}$ -complete. For each n ≥ 2, the collection of real numbers that are normal or simply normal to base n is $Π_{3}^{0}$ -complete. Moreover, $D_{ℚ}$ , the...

Note on a Theorem of Kuratowski-Sierpiński

Jana Farková (1973)

Matematický časopis

Note on limits of simply continuous and cliquish functions.

Ewert, Janina (1994)

International Journal of Mathematics and Mathematical Sciences

Note zu dem Aufsatze "über eine Eigenschaft von Functionaldeterminanten" Bd. 69, p. 355 dieses Journals.

A. Clebsch (1869)

Journal für die reine und angewandte Mathematik

Notes on an approximate derivative

Ladislav Mišík (1972)

Matematický časopis

On a problem concerning uniform ;imits of Darboux functions

J. Smítal (1971)

Colloquium Mathematicae

On a theorem of Holický and Zelený concerning Borel maps without $σ$ -compact fibers

P. Milewski, Roman Pol (2003)

Czechoslovak Mathematical Journal

The paper is concerned with a recent very interesting theorem obtained by Holický and Zelený. We provide an alternative proof avoiding games used by Holický and Zelený and give some generalizations to the case of set-valued mappings.