Concerning continuous collections of continuous curves

Concerning Simple Continuous Curves

Various definitions of simple continuous arcs and closed curves have been given, f The definitions of arcs usually contain the requirement that the point-set in question should be bounded. In attempting to prove that every interval t of an open curve as defined in a recent paper \ is a simple continuous arc, while I found it easy to prove that t satisfies all the other requirements of Janiszews...

Continuous Collections of Continuous Curves in the Plane

The purpose of this paper is to consider the class of continuous collections of mutually exclusive compact continuous curves in the plane. Throughout this paper we shall denote by G or G with a subscript or superscript a collection of this class with the property that G with respect to its elements as points is a nondegenerate compact closed point set. G has then the significance of being both ...

On Spaces Filled up by Continuous Collections of Atriodic Continuous Curves

Throughout this paper, G will denote a nondegenerate continuous collection of atriodic continuous curves (i.e. arcs or simple closed curves) filling up a compact metric continuum M. As is well known, we may regard G itself as a compact metric continuum, with the elements of the collection G as the points of the space G and with G, as a space, the image of M under an open continuous mapping whos...

Concerning Certain Linear Abstract Spaces and Simple Continuous Curves*

The first section of this paper is given over mainly to the investigation of linear Hausdorff spaces. However, the principal object of the paper is to characterize topologically that class of point sets used in the geometry for lines, namely, the class of simple continuous curves. This has already been done by R. L. Moore,f by R. L. Wilder, | and by myself.§ The results of this paper generalize...

Concerning Rings of Continuous Functions