Extending binary operations to funtor-spaces
Given a continuous monadic functor $T:\mathbf{Comp}\to\mathbf{Comp}$ in the category of compacta and a discrete topological semigroup $X$ we extend the semigroup operation $\varphi:X\times X\to X$ to a right-topological semigroup operation $\Phi:T\beta X\times T\beta X\to T\beta X,$ whose topologica...
Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
Vasyl Stefanyk Precarpathian National University
2013-01-01
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Series: | Karpatsʹkì Matematičnì Publìkacìï |
Online Access: | http://journals.pu.if.ua/index.php/cmp/article/view/23 |
Summary: | Given a continuous monadic functor $T:\mathbf{Comp}\to\mathbf{Comp}$ in the category of compacta and a discrete topological semigroup $X$ we extend the semigroup operation $\varphi:X\times X\to X$ to a right-topological semigroup operation $\Phi:T\beta X\times T\beta X\to T\beta X,$ whose topological center $\Lambda_\Phi$ contains the dense subsemigroup $T_f X$ consisting of elements $a\in T\beta X$ that have finite support in $X$. |
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ISSN: | 2075-9827 2313-0210 |