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Let K be a subfield of the real field, D ⊆ K be a discrete set and f: Dⁿ → K be such that f(Dⁿ) is somewhere dense. Then (K,f) defines ℤ. We present several applications of this result. We show that K expanded by predicates for different cyclic multiplicative subgroups defines ℤ. Moreover, we prove that every definably complete expansion of a subfield of the real field satisfies an analogue of the Baire category theorem.

Expansive Automorphisms in Compact Groups.

T.S. Wu (1966)

Mathematica Scandinavica

Expansive collections of continua

Donald E. Bennett (1978)

Commentationes Mathematicae Universitatis Carolinae

Expansive homeomorphisms and indecomposability

Hisao Kuto (1991)

Fundamenta Mathematicae

Expansive transformation semigroups of endomorphisms

Murray Eisenberg (1966)

Fundamenta Mathematicae

Expansiveness on Compact Piecewise Linear Manifolds.

Akira Kroyama (1981)

Mathematische Zeitschrift

Exponentiability in homotopy slices of TOP and pseudo-slices of CAT.

Niefield, Susan (2007)

Theory and Applications of Categories [electronic only]

Exponentiability in lax slices of $𝒯 o p$ .

Niefield, Susan (2006)

Theory and Applications of Categories [electronic only]

Exponentiability of perfect maps: Four approaches.

Niefield, Susan (2002)

Theory and Applications of Categories [electronic only]

Exponentiable embeddings in totally reflective subcategories of $T O P$

F. Cagliari, S. Mantovani (1990)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Exponentiable morphisms: Posets, spaces, locales, and Grothendieck toposes.

Niefield, Susan (2001)

Theory and Applications of Categories [electronic only]

Exponential domination in function spaces

Vladimir Vladimirovich Tkachuk (2020)

Commentationes Mathematicae Universitatis Carolinae

Given a Tychonoff space $X$ and an infinite cardinal $κ$ , we prove that exponential $κ$ -domination in $X$ is equivalent to exponential $κ$ -cofinality of $C_{p} (X)$ . On the other hand, exponential $κ$ -cofinality of $X$ is equivalent to exponential $κ$ -domination in $C_{p} (X)$ . We show that every exponentially $κ$ -cofinal space $X$ has a $κ^{+}$ -small diagonal; besides, if $X$ is $κ$ -stable, then $n w (X) \leq κ$ . In particular, any compact exponentially $κ$ -cofinal space has weight not exceeding $κ$ . We also establish that any exponentially $κ$ -cofinal space $X$ with...

Exponential law for uniformly continous proper maps.

R. Ayala, E. Dominguez, A. Quintero (1988)

Publicacions Matemàtiques

The purpose of this note is to prove the exponential law for uniformly continuous proper maps.

Exponential objects in the construct $𝑃𝑅𝐴𝑃$

E. Lowen, R. Lowen, C. Verbeeck (1997)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Exponential separability is preserved by some products

Vladimir Vladimirovich Tkachuk (2022)

Commentationes Mathematicae Universitatis Carolinae

We show that exponential separability is an inverse invariant of closed maps with countably compact exponentially separable fibers. This implies that it is preserved by products with a scattered compact factor and in the products of sequential countably compact spaces. We also provide an example of a $σ$ -compact crowded space in which all countable subspaces are scattered. If $X$ is a Lindelöf space and every $Y \subset X$ with $| Y | \leq 2^{ω_{1}}$ is scattered, then $X$ is functionally countable; if every $Y \subset X$ with $| Y | \leq 2^{𝔠}$ is scattered, then...

Exponentially Complete Spaces II

M. M. Marjanović (1972)

Publications de l'Institut Mathématique

Exponentially complete spaces II.

M.M. Marjanovic (1972)

Publications de l'Institut Mathématique [Elektronische Ressource]

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