Remark on Continuous Collections

Continuous Collections of Decomposable Continua on a Spherical Surface

In this paper a study is made of continuous collections of decomposable continua on a spherical surface. Properties of the decomposition spaces of such collections filling up continua are established, and a characterization of the decomposition spaces of such collections filling up a spherical surface is obtained. The results of the present paper are related to certain results obtained by R. D....

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...

Remark on Taylor's Formula

does not contain any point of Er other than p. Cp(r]) is defined as in (5). From this it can be shown that Er has finite (n —1)-dimensional measure. Let us not assume now that r is large. We then write E = UjLxE^ where the E's are closed and their diameter is less than €. Then, by what has been shown before, if e is small enough Ef* has finite (w —1)-dimensional measure. Clearly ErCUjLxE?^'. Bu...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem