Pointwise density topology

Lambda-topology vs. Pointwise Topology

This paper deals with families of conformal iterated function systems (CIFS). The space CIFS(X, I) of all CIFS, with common seed space X and alphabet I, is successively endowed with the topology of pointwise convergence and the so-called λ-topology. We show just how bad the topology of pointwise convergence is: although the Hausdorff dimension function is continuous on a dense Gδ-set, it is als...

POINTWISE CONVERGENCE TOPOLOGY AND FUNCTION SPACES IN FUZZY ANALYSIS

We study the space of all continuous fuzzy-valued functions  from a space $X$ into the space of fuzzy numbers $(mathbb{E}sp{1},dsb{infty})$  endowed with the pointwise convergence topology.   Our results generalize the classical ones for  continuous real-valued functions.   The field of applications of this approach seems to be large, since the classical case  allows many known devices to be fi...

Adaptive pointwise estimation of conditional density function

Note on function spaces with the topology of pointwise convergence

The note contains two examples of function spaces Cp(X) endowed with the pointwise topology. The first example is Cp(M),M being a planar continuum, such that Cp(M) is uniformly homeomorphic to Cp(M) if and only ifm = n. This strengthens earlier results concerning linear homeomorphisms. The second example is a non-Lindelöf function space Cp(X), whereX is a monolithic perfectly normal compact spa...

Group-valued Continuous Functions with the Topology of Pointwise Convergence

Let G be a topological group with the identity element e. Given a space X, we denote by Cp(X,G) the group of all continuous functions from X to G endowed with the topology of pointwise convergence, and we say that X is: (a) G-regular if, for each closed set F ⊆ X and every point x ∈ X \ F , there exist f ∈ Cp(X,G) and g ∈ G \ {e} such that f(x) = g and f(F ) ⊆ {e}; (b) G-regular provided that t...