Displaying similar documents to “On the imbedding of subsets of a metric space in Jordan continua”

Concerning continuous curves

R. Wilder (1925)

Fundamenta Mathematicae

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The present paper has three main objects: 1. to study the analogy between ordinary two-dimensional space and a plane continuous curve; 2. to characterize and analyze the boundaries of the domains complementary to a plane continuous curve; 3. to give a new characterization of continuous curves suitable for any number of dimensions;

Concerning the common boundary of two domains

R. Moore (1924)

Fundamenta Mathematicae

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The main purpose of the present paper is to show that if a bounded continuum has more then one prime part and no one of its prime parts separates the plane then in order that it should have just two complementary domains and be the complete boundary of each of them it is necessary and sufficient that it should remain connected in the weak sense on the removal of any one of its connected proper subsets which is closed.