Homomorphisms of nearrings of continuous functions from topological spaces into the asymmetric nearring

✍ Scribed by K.D. Magill; Jr

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 131 KB
• Volume: 95
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(98)00011-x

✦ Synopsis

There is a unique (up to isomorphism) topological nearring N , whose additive group is the twodimensional Euclidean group, which has an identity but is not zero symmetric. For any topological space X, we denote by N (X) the nearring of all continuous functions from X to N where the operations on N (X) are the pointwise operations. We determine all the homomorphisms from the nearring N (X) into N (Y ) when X is realcompact and Y is completely regular and Hausdorff. This result is then used to show that if both X and Y are either compact and Hausdorff or realcompact generated spaces then the endomorphism semigroups of N (X) and N (Y ) are isomorphic if and only if the spaces X and Y are homeomorphic.