Geodesic
Liouville's theorem for vector-valued functions
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2013), pp. 5-16

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It is shown in [2] that any $X$-valued analytic map on $\mathbb C\cup\{\infty\}$ is a constant map in case when $X$ is a strongly galbed Hausdorff space. In [3] this result is generalized to the case when $X$ is a topological linear Hausdorff space, the von Neumann bornology of which is strongly galbed. A new detailed proof for the last result is given in the present paper. Moreover, it is shown that for several topological linear spaces the von Neumann bornology is strongly galbed or pseudogalbed. 
@article{BASM_2013_2_a1,
     author = {Mati Abel},
     title = {Liouville's theorem for vector-valued functions},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {5--16},
     publisher = {mathdoc},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2013_2_a1/}
}
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Mati Abel. Liouville's theorem for vector-valued functions. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2013), pp. 5-16. http://geodesic.mathdoc.fr/item/BASM_2013_2_a1/