Removing Sets from Connected Spaces While Preserving Connectedness

Authors

Melvin Henriksen, Harvey Mudd CollegeFollow
Amir Nikou, Chamran University

Document Type

Article

Department

Mathematics (HMC)

Publication Date

2007

Abstract

As per the title, the nature of sets that can be removed from a product of more than one connected, arcwise connected, or point arcwise connected spaces while preserving the appropriate kind of connectedness is studied. This can depend on the cardinality of the set being removed or sometimes just on the cardinality of what is removed from one or two factor spaces. Sometimes it can depend on topological properties of the set being removed or its trace on various factor spaces. Some of the results are complicated to prove while being easy to state. Sometimes proofs for different kinds of connectedness are similar, but different enough to require separate proofs. Many examples are given to show that part of the hypotheses of theorems cannot be dropped, and some examples describe results about spaces whose connectedness can be established directly but not with the help of our results. A large number of examples are given for such purposes.

Comments

Previously linked to as: http://ccdl.libraries.claremont.edu/u?/irw,436.

Publisher pdf, posted with permission.

Article can also be found at http://dml.cz/dmlcz/119643

Rights Information

© 2007 Charles University in Prague

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Recommended Citation

Henriksen, Melvin, and Amir Nikou. "Removing sets from connected spaces while preserving connectedness." Commentationes Mathematicae Universitatis Carolinae 48.1 (2007): 119-134.