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A. D. Myskis assemblage axiom 9 axiom of countability bicompact boundary element boundary points Caratheodory cofinal compact completely regular end completely regular space condition Mj connected components consider continuous function converge cross-cut defined definition denoted descriptive boundary 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 Hausdorff space hence homeomorphism inclusion and set Kaufmann limit point line segment 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 polygonal line prime-ends proof of theorem quasi-limit point quence regular centralized family resulting directed set satisfies axiom satisfies conditions Sbornik N.S. sequences of points set G set in correspondence simply connected strength of condition T2-space tion topological space Uber wide sense