#### Document Type

Conference Proceeding

#### Language

eng

#### Format of Original

5 p.

#### Publication Date

1-1976

#### Publisher

American Mathematical Society

#### Source Publication

Proceedings of the American Mathematical Society

#### Source ISSN

0002-9939

#### Original Item ID

doi: 10.1090/S0002-9939-1976-0405332-5; Shelves: QA1 .A5215 Storage S

#### Abstract

Let *X* be a space and let *H(X)* denote its hyperspace (= all nonempty closed subsets of *X* topologized via the Vietoris topology). Then *X* is Boolean (= totally disconnected compact Hausdorff) iff is Boolean; and if *B* denotes the characteristic algebra of clopen sets in *X* then the corresponding algebra for *H(X)* is the free algebra generated by *B* modulo the ideal which "remembers" the upper semilattice structure of* B*.

#### Recommended Citation

Bankston, Paul, "Clopen Sets in Hyperspace" (1976). *Mathematics, Statistics and Computer Science Faculty Research and Publications*. 147.

https://epublications.marquette.edu/mscs_fac/147

## Comments

Published version.

Proceedings of the American Mathematical Society, Vol. 54, No. 1 (January 1976): 298-302. DOI. © 1976 American Mathematical Society. Used with permission.