New concepts in the theory of topological space—supercondensed set, subcondensed set, and condensed set

Yoshinori Isomichi

Vol. 38 (1971), No. 3, 657–668

DOI: 10.2140/pjm.1971.38.657

Abstract

A set which satisfies A^ai = Aⁱ(A^ia = A^a) is named a supercondensed (subcondensed) set. A supercondensed and subcondensed set is named a condensed set. Theorems about these new concepts are discussed in this paper.

Sets of the topological space are classified into three classes by comparing A^ai and A^ia.

Mathematical Subject Classification 2000

Primary: 54B05

Milestones

Received: 23 November 1970

Published: 1 September 1971