Quote: a cut separates a continuum into multiple continuums by removing one or more elements

Quotation

A cut is removing one or more elements from a continuum. It separates the continuum into multiple continuums. A continuum, C, is one dimensional if it] may be subdivided by a cut reducing to a finite number of elements, all distinguishable the one from the other ... If, on the contrary, C can only be subdivided by cuts which are themselves continuums, we shall say that C is of several dimensions; if the cuts are continuums of one dimension, then we shall say that C has two dimensions ...   Google-1   Google-2

Published before 1923

Additional Titles

Quote: a continuum has two dimensions if it is cut by one-dimensional continuums

Related Topics

Topic: continuum in mathematics (7 items)