On the continuity of nearly continuous linear and bilinear mappings
1 Department of Mathematical Analysis, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine
Keywords:
bilinear mappings
Abstract
We prove that every bilinear somewhat continuous at some point mapping
f
:
X
×
Y
→
Z
,
where
X, Y, Z
are arbitrary topological vector spaces, is continuous. If, moreover, the space
Z
is
locally bounded then every locally bounded at some point bilinear mapping
f
:
X
×
Y
→
Z
is
continuous.
Cite
- ACS Style
- Maslyuchenko, V.K.; Rovenko , N.M. On the continuity of nearly continuous linear and bilinear mappings. Bukovinian Mathematical Journal. 2016, 2
- AMA Style
- Maslyuchenko VK, Rovenko NM. On the continuity of nearly continuous linear and bilinear mappings. Bukovinian Mathematical Journal. 2016; 2(4).
- Chicago/Turabian Style
- Volodymyr Kyrylovych Maslyuchenko, N. M. Rovenko . 2016. "On the continuity of nearly continuous linear and bilinear mappings". Bukovinian Mathematical Journal. 2 no. 4.
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