$\mathrm{HL}$-Differentiability is Equivalent to $\mathrm{MB}^\sharp$-Differentiability

I. Vodova

Mathematical Institute, Silesian University in Opava

Abstract: In 1972, it was announced by Averbukh and Smolyanov that $\mathrm{HL}$-differentiability is equivalent to $\mathrm{FB}^\sharp$-differentiability. The proof has not been published till now. Here we prove a stronger result, namely, the one formulated in the title.

Keywords: filter, pseudotopology, differentiability, differentiability in the sense of Frölicher and Bucher, in the sense of Michael and Bastiani, and in the sense of Hyers and Lang.

UDC: 517.2+517.98

Received: 27.01.2010

DOI: 10.4213/mzm8745

 English version: Mathematical Notes, 2010, 87:6, 807–810

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