## I. On the concept of boundary: II. The definition of a boundary by means of continuous mappings. III. On the equivalence of certain methods of a boundary. (Matematĭceskiĭ sbornik n. s. 25(67), 387-414 (1949); 26(68), 225-227 (1950); 26(68), 228-236 (1950)) |

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A. D. Myskis assemblage axiom 9 axiom of countability boundary element boundary points Caratheodory's cofinal compact completely regular end connected components consider continuous function Continuous Mappings converge cross-cut defined definition denoted Dirichlet problem domain G dual to axiom E. H. Moore easy to verify equivalent everywhere dense example finite number follows immediately fulfillment of axiom fulfillment of condition G M(N H. L. Smith Hausdorff space hence homeomorphism inclusion and set Kappos Kaufmann Let G limit point line segment locally bicompact Math Mazurkiewicz metric space narrow sense natural mapping necessary and sufficient necessity of condition neighborhood non-void open sets order to prove P. S. Aleksandrov Perkins prime-ends proof of theorem quasi-limit point regular centralized family resulting directed set satisfies axiom satisfies conditions sequences of points set G set in correspondence simply connected strength of condition T2-space tion topological space Uber wide sense