{"product_id":"exponential-algebra-as-an-extension-of-topological-algebra-von-prithwiraj-halder","title":"Exponential Algebra: As an Extension of Topological Algebra","description":"\u003cp\u003eIn this book, we have introduced the concept of `\\textit{exponential algebra}' (in short \\textit{ealg}) by defining an internal multiplication on an evs over some field $ K $. We have explained that the concept of exponential algebra can be thought of as a generalisation of `algebra' in the sense that every exponential algebra contains an algebra; conversely, any algebra can be embedded into an exponential algebra. We develop a quotient structure on an ealg $X$ over some field $K$ by using the concept of congruence and topologise it. We introduce the concept of \\emph{ideal}, \\emph{semiideal} and \\emph{maximal ideal} of an ealg. We have shown that the hyperspace $\\com{\\X}{}$ (the set of all nonempty compact subsets of a Hausdorff topological algebra $\\X$) is a topological exponential algebra over the field $\\K$ of real or complex. We explore the function spaces in light of exponential algebra. It has been shown that the space of positive measures $\\mathscr M(G)$ on a locally compact Housdorff topological group $G$, which are finite on each compact subset of $G$ is a topological ealg. Finally, we found a topological ealg with the help of Hausdorff metric.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9786206146797\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9786206146797","offer_id":46364877979973,"sku":"9786206146797","price":60.9,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/5f335cf4-9cff-40c6-9db6-e33ba81050ed.jpg?v=1773212389","url":"https:\/\/shop.autorenwelt.de\/products\/exponential-algebra-as-an-extension-of-topological-algebra-von-prithwiraj-halder","provider":"Autorenwelt Shop","version":"1.0","type":"link"}