Vol. 38, No. 3, 1971

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Separating certain plane-like spaces by Peano continua

John William Green

Vol. 38 (1971), No. 3, 625–634

Suppose S is a connected, locally connected, complete Moore space having no cut point and in which the Jordan Curve Theorem holds. Thus, suppose S satisfies R. L. Moore’s Axioms 0,1 4. Certain extensions and applications of earlier results of the author are established. In particular, modified forms of the Torhorst theorem and a plane theorem of R. L. Moore are shown to hold in the space S, two theorems concerning the separation of S by compact dendrons are extended to Peano continua and another to certain Menger regular curves. Finally, a general method of constructing certain pathological spaces is given.

Mathematical Subject Classification
Primary: 54F20
Received: 14 September 1970
Published: 1 September 1971
John William Green