A NOTE ON POSITIVELY EXPANSIVE MAPS ON NON-COMPACT SPACES

Purchase PDF

Published: 2016-01-23

Page: 57-60


U. V. CHETANA *

Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, Karnataka, India.

B. R. SHANKAR

Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, Karnataka, India.

*Author to whom correspondence should be addressed.


Abstract

Expansive homeomorphisms and positively expansive maps occur frequently in dynamical systems. In compact spaces, positively expansive maps cannot be injective. In non-compact spaces they may or may not be injective, and an element can have any prescribed number of pre-images, even when the space is totally bounded and perfect. An example is given to clarify this.

Keywords: Discrete;, compact;, positively expansive.


How to Cite

CHETANA, U. V., & SHANKAR, B. R. (2016). A NOTE ON POSITIVELY EXPANSIVE MAPS ON NON-COMPACT SPACES. Asian Journal of Mathematics and Computer Research, 11(1), 57–60. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/370

Downloads

Download data is not yet available.