Continuous selections of multivalued mappings

This survey covers in our opinion the most important results in the theory of continuous selections of multivalued mappings (approximately) from 2002 through 2012. It extends and continues our previous such survey which appeared in Recent Progress in General Topology, II, which was published in 2002. In comparison, our present survey considers more restricted and specific areas of mathematics. Note that we do not consider the theory of selectors (i.e. continuous choices of elements from subsets of topological spaces) since this topics is covered by another survey in this volume

On small homotopies of loops

Two natural questions are answered in the negative: (1) If a space has the property that small nulhomotopic loops bound small nulhomotopies, then are loops which are limits of nulhomotopic loops themselves nulhomotopic? (2) Can adding arcs to a space cause an essential curve to become nulhomotopic? The answer to the first question clarifies the relationship between the notions of a space being homotopically Hausdorff and $\pi_1$-shape injective.Comment: 12 pages, 5 figure

On linearly ordered HH-closed topological semilattices

We give a criterium when a linearly ordered topological semilattice is $H$-closed. We also prove that any linearly ordered $H$-closed topological semilattice is absolutely $H$-closed and we show that every linearly ordered semilattice is a dense subsemilattice of an $H$-closed topological semilattice

On chains in HH-closed topological pospaces

We study chains in an $H$-closed topological partially ordered space. We give sufficient conditions for a maximal chain $L$ in an $H$-closed topological partially ordered space such that $L$ contains a maximal (minimal) element. Also we give sufficient conditions for a linearly ordered topological partially ordered space to be $H$-closed. We prove that any $H$-closed topological semilattice contains a zero. We show that a linearly ordered $H$-closed topological semilattice is an $H$-closed topological pospace and show that in the general case this is not true. We construct an example an $H$-closed topological pospace with a non-$H$-closed maximal chain and give sufficient conditions that a maximal chain of an $H$-closed topological pospace is an $H$-closed topological pospace.Comment: We have rewritten and substantially expanded the manuscrip

Integrated cross-domain object storage in working memory: Evidence from a verbal-spatial memory task

Working-memory theories often include domain-specific verbal and visual stores (e.g., the phonological and visuospatial buffers of Baddeley, 1986), and some also posit more general stores thought to be capable of holding verbal or visuospatial materials (Baddeley, 2000; Cowan, 2005). However, it is currently unclear which type of store is primarily responsible for maintaining objects that include components from multiple domains. In these studies, a spatial array of letters was followed by a single probe identical to an item in the array or differing systematically in spatial location, letter identity, or their combination. Concurrent verbal rehearsal suppression impaired memory in each of these trial types in a task that required participants to remember verbal-spatial binding, but did not impair memory for spatial locations if the task did not require verbal-spatial binding for a correct response. Thus, spatial information might be stored differently when it must be bound to verbal information. This suggests that a cross-domain store such as the episodic buffer of Baddeley (2000) or the focus of attention of Cowan (2001) might be used for integrated object storage, rather than the maintenance of associations between features stored in separate domain-specific buffers

On extending actions of groups

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications