Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Mathematics
Openness Of Induced Projections, J. J. Charatonik, W. J. Charatonik, Alejandro Illanes
Openness Of Induced Projections, J. J. Charatonik, W. J. Charatonik, Alejandro Illanes
Mathematics and Statistics Faculty Research & Creative Works
For continua X and Y it is shown that if the projection f : X x Y ->X has its induced mapping C(f) open, then X is C*-smooth. As a corollary, a characterization of dendrites in these terms is obtained.
Some Applications Of The Ultrapower Theorem To The Theory Of Compacta, Paul Bankston
Some Applications Of The Ultrapower Theorem To The Theory Of Compacta, Paul Bankston
Mathematics, Statistics and Computer Science Faculty Research and Publications
The ultrapower theorem of Keisler and Shelah allows such model-theoretic notions as elementary equivalence, elementary embedding and existential embedding to be couched in the language of categories (limits, morphism diagrams). This in turn allows analogs of these (and related) notions to be transported into unusual settings, chiefly those of Banach spaces and of compacta. Our interest here is the enrichment of the theory of compacta, especially the theory of continua, brought about by the importation of model-theoretic ideas and techniques.
Dendrites And Light Open Mappings, J. J. Charatonik, W. J. Charatonik, Pawel Krupski
Dendrites And Light Open Mappings, J. J. Charatonik, W. J. Charatonik, Pawel Krupski
Mathematics and Statistics Faculty Research & Creative Works
It is shown that a metric continuum X is a dendrite if and only if for every compact space Y and for every light open mapping f : Y ->f(Y ) such that X c f(Y ) there is a copy X1 of X in Y for which the restriction fjX1 : X1 ->X is a homeomorphism. Another characterization of dendrites in terms of continuous selections of multivalued functions is also obtained.