Exponentiation in Rings

R. H. Redfield

Type: Article

Publication Date: 1995-01-01

Citations: 0

DOI: https://doi.org/10.2307/2974855

Abstract

For a Heyting algebra V which, as a category, is monoidal closed, we obtain characterizations of exponentiable objects and morphisms in the category of V-categories and apply them to some well-known examples.In the case V = R + these characterizations of exponentiable morphisms and objects in the categories (P)Met of (pre)metric spaces and non-expansive maps show in particular that exponentiable metric spaces are exactly the almost convex metric spaces, while exponentiable complete metric spaces are the complete totally convex ones.

Locations

American Mathematical Monthly - View
Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Almost ring theory - sixth release	2002	Ofer Gabber Lorenzo Ramero
+	Adic spaces II	2020	Peter Scholze Jared Weinstein
+	Affine geometry of vector spaces over rings	1942	Cath Everett
+	Locally convex topologies on rings of continuous functions	1973	A. G. A. G. Babiker
+	K-algebras and K-spaces of constant type with indefinite metric	1981	В. Ф. Кириченко
+	Tropical Geometry	2008	Eva María Feichtner Andreas Gathmann Ilia Itenberg Thorsten Theobald
+ PDF Chat	Rings with Hausdorff structure space	1958	Leonard Gillman
+	Locally bounded topologies on Euclidean rings	1978	Witold Więsław
+	On ringed spaces	1970	Christopher J. Mulvey
+	A Note on Near-Rings Over Vector Spaces	1967	R. E. Williams
+	Stably Euclidean Rings	2011
+	Bi-Lipschitz Maps in Q-regular Loewner Spaces	2008	Ke Ke Ying Ying Chen Nong Fang
+	Exponential maps and λ-rings	1983	Peter Hoffman
+	Structure spaces for rings of continuous functions with applications to realcompactifications	1997	Lothar Redlin Saleem Watson
+	Characterization of almost semi-Heyting algebra	2020	S. Ramesh M. V. Ratnamani V.V.V.S.S.P.S. Srikanth
+ PDF Chat	RINGS AND QUASICONFORMAL MAPPINGS IN SPACE	1961	F. W. Gehring
+ PDF Chat	Rings and Quasiconformal Mappings in Space	1962	F. W. Gehring
+ PDF Chat	Rings and quasiconformal mappings in space	1962	F. W. Gehring
+ PDF Chat	Structure spaces of rings and Banach algebras.	1984	Bertram Yood
+	Fully Closed and Ring-Like Maps	2019	Michael G. Charalambous

Works That Cite This (0)

Action	Title	Year	Authors

Works Cited by This (8)

Action	Title	Year	Authors
+	Exponentiability in categories of lax algebras	2003	Maria Manuel Clementino Dirk Hofmann Walter Tholen
+	Cartesianness: topological spaces, uniform spaces, and affine schemes	1982	Susan Niefield
+ PDF Chat	Extension of uniformly continuous transformations and hyperconvex metric spaces	1956	N. Aronszajn Prom Panitchpakdi
+	Exponentiable morphisms, partial products and pullback complements	1987	Roy Dyckhoff Walter Tholen
+	An algebraic description of regular epimorphisms in topology	2005	Dirk Hofmann
+	Metric spaces, generalized logic, and closed categories	1973	F. William Lawvere
+	Metric, topology and multicategory—a common approach	2003	Maria Manuel Clementino Walter Tholen
+	The convergence approach to exponentiable maps.	2003	Maria Manuel Clementino Dirk Hofmann Walter Tholen