Local compactness in approach spaces. II.
Local compactness in bitopological hyperspace
Local connectedness, connectedness im kleinen, and another properties of hyperspaces of spaces
Local connectivity, open homogeneity and hyperspaces.
In the first part of the paper behavior of conditions related to local connectivity at a point is discussed if the space is transformed under a mapping that is interior or open at the considered point of the domain. The second part of the paper deals with metric locally connected continua. They are characterized as continua for which the hyperspace of their nonempty closed subjects is homogeneous with respect to open mappings. A similar characterization for the hyperspace of subcontinua remains...
Local extension of maps.
Local semigroups
Localization In Bundles Of Metric Spaces,
Localization in Bundles of uniform spaces
Localization with change of the base space in uniform bundles and sheaves.
Locally connected curves viewed as inverse limits
Locally connected images of ordered compacta
Locally Sierpinski Quotients.
Locally starlike decompositions of separable metric spaces
Locating cones and Hubert cubes in hyperspaces
MAD families and -points
The Katětov ordering of two maximal almost disjoint (MAD) families and is defined as follows: We say that if there is a function such that for every . In [Garcia-Ferreira S., Hrušák M., Ordering MAD families a la Katětov, J. Symbolic Logic 68 (2003), 1337–1353] a MAD family is called -uniform if for every , we have that . We prove that CH implies that for every -uniform MAD family there is a -point of such that the set of all Rudin-Keisler predecessors of is dense in the...
Making holes in the cone, suspension and hyperspaces of some continua
A connected topological space is unicoherent provided that if where and are closed connected subsets of , then is connected. Let be a unicoherent space, we say that makes a hole in if is not unicoherent. In this work the elements that make a hole to the cone and the suspension of a metric space are characterized. We apply this to give the classification of the elements of hyperspaces of some continua that make them hole.
Mapping approximate inverse systems of compacta
Mapping theorems on countable tightness and a question of F. Siwiec
In this paper -quotient maps and -spaces are introduced. It is shown that (1) countable tightness is characterized by -quotient maps and quotient maps; (2) a space has countable tightness if and only if it is a countably bi-quotient image of a locally countable space, which gives an answer for a question posed by F. Siwiec in 1975; (3) -spaces are characterized as the -quotient images of metric spaces; (4) assuming , a compact -space is an -space if and only if every countably compact subset...
Mappings covered by products and pinched products
Mappings on -paracompact spaces.