Displaying similar documents to “A note on f.p.p. and f * . p . p .

Functions characterized by images of sets

Krzysztof Ciesielski, Dikran Dikrajan, Stephen Watson (1998)

Colloquium Mathematicae

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For non-empty topological spaces X and Y and arbitrary families 𝒜 𝒫 ( X ) and 𝒫 ( Y ) we put 𝒞 𝒜 , =f ∈ Y X : (∀ A ∈ 𝒜 )(f[A] ∈ ) . We examine which classes of functions Y X can be represented as 𝒞 𝒜 , . We are mainly interested in the case when = 𝒞 ( X , Y ) is the class of all continuous functions from X into Y. We prove that for a non-discrete Tikhonov space X the class = 𝒞 (X,ℝ) is not equal to 𝒞 𝒜 , for any 𝒜 𝒫 ( X ) and 𝒫 (ℝ). Thus, 𝒞 (X,ℝ) cannot be characterized by images of sets. We also show that none of the following...

On the vanishing of Iwasawa invariants of absolutely abelian p-extensions

Gen Yamamoto (2000)

Acta Arithmetica

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1. Introduction. Let p be a prime number and p the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, k a p -extension of k, k n the nth layer of k / k , and A n the p-Sylow subgroup of the ideal class group of k n . Iwasawa proved the following well-known theorem about the order A n of A n : Theorem A (Iwasawa). Let k / k be a p -extension and A n the p-Sylow subgroup of the ideal class group of k n , where k n is the n th layer of k / k . Then there exist integers λ = λ ( k / k ) 0 , μ = μ ( k / k ) 0 , ν = ν ( k / k ) , and n₀ ≥ 0...

Topological structure of the space of lower semi-continuous functions

Katsuro Sakai, Shigenori Uehara (2006)

Commentationes Mathematicae Universitatis Carolinae

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Let L ( X ) be the space of all lower semi-continuous extended real-valued functions on a Hausdorff space X , where, by identifying each f with the epi-graph epi ( f ) , L ( X ) is regarded the subspace of the space Cld F * ( X × ) of all closed sets in X × with the Fell topology. Let LSC ( X ) = { f L ( X ) f ( X ) , f ( X ) ( - , ] } and LSC B ( X ) = { f L ( X ) f ( X ) is a bounded subset of } . We show that L ( X ) is homeomorphic to the Hilbert cube Q = [ - 1 , 1 ] if and only if X is second countable, locally compact and infinite. In this case, it is proved that ( L ( X ) , LSC ( X ) , LSC B ( X ) ) is homeomorphic to ( Cone Q , Q × ( 0 , 1 ) , Σ × ( 0 , 1 ) ) (resp. ( Q , s , Σ ) ) if X is compact (resp. X is non-compact), where Cone Q = ( Q × 𝐈 ) / ( Q × { 1 } ) is...

Guidance properties of a cylindrical defocusing waveguide

Oldřich John, Charles A. Stuart (1994)

Commentationes Mathematicae Universitatis Carolinae

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We discuss the propagation of electromagnetic waves of a special form through an inhomogeneous isotropic medium which has a cylindrical symmetry and a nonlinear dielectric response. For the case where this response is of self-focusing type the problem is treated in [1]. Here we continue this study by dealing with a defocusing dielectric response. This tends to inhibit the guidance properties of the medium and so guidance can only be expected provided that the cylindrical stratification...

On locally r -incomparable families of infinite-dimensional Cantor manifolds

Vitalij A. Chatyrko (1999)

Commentationes Mathematicae Universitatis Carolinae

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The notion of locally r -incomparable families of compacta was introduced by K. Borsuk [KB]. In this paper we shall construct uncountable locally r -incomparable families of different types of finite-dimensional Cantor manifolds.

Baireness of C k ( X ) for ordered X

Michael Granado, Gary Gruenhage (2006)

Commentationes Mathematicae Universitatis Carolinae

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We show that if X is a subspace of a linearly ordered space, then C k ( X ) is a Baire space if and only if C k ( X ) is Choquet iff X has the Moving Off Property.