Analysis in Linear Topological Spaces

Citation

Paxson, Edwin Woolman (1937) Analysis in Linear Topological Spaces. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/j0h4-j979. https://resolver.caltech.edu/CaltechTHESIS:07052023-222228608

Abstract

During the past five years the study of linear topological spaces, those non-metrisable spaces intermediate between the pure spaces of ensemble topology and the normed spaces of General Analysis, has received much attention, particularly under the hands of the Russian and Polish schools headed by Kolmogoroff and Tychonoff. Interest in the slightly weaker spaces of topological group type has also been greatly stimulated by the search for strong purely topological foundations of group theory by Schreier, von Dantzig and others, and for an abstract formulation of continuous group theory as in the work of Michal and Elconin.

Because of the implied necessity of theories in the large for situations such as these, it was felt desirable to determine what analytic entities could be defined, while preserving as large a portion of the usual properties as possible, directly for the base spaces, without the rigid local intermediary of the norm.

I should like to express here my appreciation of the sustained assistance and advice of Professor A.D. Michal in the development of this thesis.

Thesis Files