CAJ | 학술논문

对距离线性空阃之间的映射可选定三个条件(O1)、(O2)与(O3),它们均与映射是不是线性的无关,也与映射有无连续点无关.利用此三条给出了第一个既不要求映射线性也不要求映射有连续点的开映射定理:距离线性空间之间的映射若满足条件(O1)、(O2)与(O3),则它是开映射.本定理的诸多推论中包括一些重要事实:如描述视觉的目视映射是非线性的开映射,距离线性空间之间的线性算子是开映射当且仅当它满足条件(O1)与(O3).
대거리선성공곤지간적영사가선정삼개조건(O1)、(O2)여(O3),타문균여영사시불시선성적무관,야여영사유무련속점무관.이용차삼조급출료제일개기불요구영사선성야불요구영사유련속점적개영사정리:거리선성공간지간적영사약만족조건(O1)、(O2)여(O3),칙타시개영사.본정리적제다추론중포괄일사중요사실:여묘술시각적목시영사시비선성적개영사,거리선성공간지간적선성산자시개영사당차부당타만족조건(O1)여(O3).
For mappings between metric linear spaces, we find conditions (O1), (O2) and (O3) which are independent of either linearity or continuity of concerned mappings. Then we have an essential improvement of the existing open mapping theorems as follows: If (O1), (O2) and (O3) hold for a mapping between metric linear spaces, then this is an open mapping. This result implies that a linear op-erator between metric linear spaces is open if and only if (O1) and (O3) hold for this operator, and for every Banach space X the important special mapping named eyeshot to X is nonlinear and open.