A Note on Pointwise Convergence

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...

A Note on Pointwise Dimensions

This short note describes a connection between algorithmic dimensions of individual points and classical pointwise dimensions of measures.

A note on convergence in fuzzy metric spaces

The sequential $p$-convergence in a fuzzy metric space, in the sense of George and Veeramani, was introduced by D. Mihet as a weaker concept than convergence. Here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. In such a case $M$ is called an $s$-fuzzy metric. If $(N_M,ast)$ is a fuzzy metri...

A Note on Subseries Convergence

A Note on Multigrid Convergence

We generalise the abstract V-cycle convergence proof of 20] and 21] to include unsymmetricsmoothing operations as well. In the case of full regularity we obtain better convergence with an increasing number of smoothing steps, thus recovering the results of 2]. Applying our theory to an anisotropic model problem we obtain optimal results in this case as well.