Geodesic
$\mathrm{HL}$-Differentiability is Equivalent to $\mathrm{MB}^\sharp$-Differentiability
Matematičeskie zametki, Tome 87 (2010) no. 6, pp. 825-829.

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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. 
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I. Vodova. $\mathrm{HL}$-Differentiability is Equivalent to $\mathrm{MB}^\sharp$-Differentiability. Matematičeskie zametki, Tome 87 (2010) no. 6, pp. 825-829. http://geodesic.mathdoc.fr/item/MZM_2010_87_6_a2/

[1] V. I. Averbukh, O. G. Smolyanov, “Differentsirovanie i psevdotopologii”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 1972, no. 1, 3–7 | MR | Zbl

[2] A. Frölicher, W. Bucher, Calculus in Vector Spaces without Norm, Lecture Notes in Math., 30, Springer-Verlag, Berlin–New York, 1966 | DOI | MR | Zbl

[3] V. I. Averbukh, O. G. Smolyanov, “Razlichnye opredeleniya proizvodnoi v lineinykh topologicheskikh prostranstvakh”, UMN, 23:4 (1968), 67–116 | MR | Zbl