In this note some necessary or/and sufficient conditions for the perturbation of a (Ω, μ)-frame are given. We also discussed (Ω, μ)-frames of subspaces.

INDEXING OF MULTIDIMENSIONAL DISCRETE DATA SPACES AND HYBRID EXTENSIONS

We propose the notion of “learning buckets”: Configurable containers of positioned learning artifacts, that teachers may include in learning designs, and that are filled during the enactment by students or teachers.

We introduce the notion of an ls-π-Ponomarev-system to give necessary and sufficient conditions for f : (M,M0) → X to be a strong wcmapping (wc-mapping, wk-mapping) where M is a locally separable metric space. Then, we systematically get characterizations of weakly continuous strong wc-images (wc-images, wk-images) of locally separable metric spaces by means of certain networks. Also, we give c...

Let p be an odd prime. We assume that all spaces are completed at p in the sense of Bousfield-Kan [2], and the cohomologies are taken with Z/pcoefficients unless otherwise specified. In this paper, we investigate the homotopy type for the loop space of an H-space whose cohomology is finitely generated as an algebra. In the case of the cohomology is finite dimensional, there is the following the...

We show that the Lorentz space Λp(w) need not be a linear set for certain “non-classical” weights w. We establish necessary and sufficient conditions on p and w for this situation to occur.