共查询到20条相似文献,搜索用时 375 毫秒
1.
For topological spaces X and Y and a metric space Z, we introduce a new class N( X ×Y, Z ) \mathcal{N}\left( {X \times Y,\,Z} \right) of mappings f: X × Y → Z containing all horizontally quasicontinuous mappings continuous with respect to the second variable. It is shown that, for
each mapping f from this class and any countable-type set B in Y, the set C
B
(f) of all points x from X such that f is jointly continuous at any point of the set {x} × B is residual in X: We also prove that if X is a Baire space, Y is a metrizable compact set, Z is a metric space, and f ? N( X ×Y, Z ) f \in \mathcal{N}\left( {X \times Y,\,Z} \right) , then, for any ε > 0, the projection of the set D
ε
(f) of all points p ∈ X × Y at which the oscillation ω
f
(p) ≥ ε onto X is a closed set nowhere dense in X. 相似文献
2.
Let A and B be Banach function algebras on compact Hausdorff spaces X and Y and let ‖.‖
X
and ‖.‖
Y
denote the supremum norms on X and Y, respectively. We first establish a result concerning a surjective map T between particular subsets of the uniform closures of A and B, preserving multiplicatively the norm, i.e. ‖Tf Tg‖
Y
= ‖fg‖
X
, for certain elements f and g in the domain. Then we show that if α ∈ ℂ {0} and T: A → B is a surjective, not necessarily linear, map satisfying ‖fg + α‖
X
= ‖Tf Tg + α‖
Y
, f,g ∈ A, then T is injective and there exist a homeomorphism φ: c(B) → c(A) between the Choquet boundaries of B and A, an invertible element η ∈ B with η(Y) ⊆ {1, −1} and a clopen subset K of c(B) such that for each f ∈ A,
$
Tf\left( y \right) = \left\{ \begin{gathered}
\eta \left( y \right)f\left( {\phi \left( y \right)} \right) y \in K, \hfill \\
- \frac{\alpha }
{{\left| \alpha \right|}}\eta \left( y \right)\overline {f\left( {\phi \left( y \right)} \right)} y \in c\left( B \right)\backslash K \hfill \\
\end{gathered} \right.
$
Tf\left( y \right) = \left\{ \begin{gathered}
\eta \left( y \right)f\left( {\phi \left( y \right)} \right) y \in K, \hfill \\
- \frac{\alpha }
{{\left| \alpha \right|}}\eta \left( y \right)\overline {f\left( {\phi \left( y \right)} \right)} y \in c\left( B \right)\backslash K \hfill \\
\end{gathered} \right.
相似文献
3.
Dorothy Maharam 《Israel Journal of Mathematics》1997,98(1):15-28
Let (X, A) be a set with a countably σ-generated “Borel” field of subsets; letW be a “Borel” subset of the product of (X, A) with the real line ℝ and its Borel fieldB; and for eachx∈X let γ
x
be a measure on the “slice”W
x={(w, t)∈W:w=x}. It is shown that, under reasonable conditions, the σ-field A⊗B|W can be generated by a real-valued functiong in such a way that, given any measurablef:W→ℝ,g can be chosen to be arbitrarily close tof and so that its “slice-integrals”
coincide with those off. This theorem is the first step in a study of monotonic sequences of countably generated σ-fields. 相似文献
4.
V. A. Zapol’skii 《Journal of Mathematical Sciences》2009,161(3):375-383
A cover of a manifold X is called an r-cover if any r points of X belong to a set in the cover. Let X and Y be two smooth manifolds, let Emb(X, Y) be the family of smooth embeddings X → Y, let M be an Abelian group, and let F: Emb(X, Y) → M be a functional. One says that the degree of F does not exceed r if for each finite open r-cover {U
i
}
i∈I
; of X there exist functionals F
i
: Emb(U
i
, Y) → M, i ∈ I, such that for each a ∈ Emb(X, Y) one has
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