Linear topological classifications of certain function spaces. II.
Linearly Singly Bi-k-spaces
Linking the closure and orthogonality properties of perfect morphisms in a category
We define perfect morphisms to be those which are the pullback of their image under a given endofunctor. The interplay of these morphisms with other generalisations of perfect maps is investigated. In particular, closure operator theory is used to link closure and orthogonality properties of such morphisms. A number of detailed examples are given.
Lipschitz continuous selectors. I: Linear selectors.
Lipschitz extensions and Lipschitz retractions in metric spaces
Lipschitz functions with unexpectedly large sets of nondifferentiability points.
Local behavior and the Vietoris and Whitehead theorems in shape theory
Local cohomological properties of homogeneous ANR compacta
In accordance with the Bing-Borsuk conjecture, we show that if X is an n-dimensional homogeneous metric ANR continuum and x ∈ X, then there is a local basis at x consisting of connected open sets U such that the cohomological properties of Ū and bd U are similar to the properties of the closed ball ⁿ ⊂ ℝⁿ and its boundary . We also prove that a metric ANR compactum X of dimension n is dimensionally full-valued if and only if the group Hₙ(X,X∖x;ℤ) is not trivial for some x ∈ X. This implies that...
Local connectedness and connected open functions.
Local connectivity and maps onto non-metrizable arcs.
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 homeomorphisms [Book]
Local homeomorphisms and related mappings on graphs
Local homeomorphisms onto tree-like continua
Local/global uniform approximation of real-valued continuous functions
For a Tychonoff space , is the lattice-ordered group (-group) of real-valued continuous functions on , and is the sub--group of bounded functions. A property that might have is (AP) whenever is a divisible sub--group of , containing the constant function 1, and separating points from closed sets in , then any function in can be approximated uniformly over by functions which are locally in . The vector lattice version of the Stone-Weierstrass Theorem is more-or-less equivalent...
Localic Katětov-Tong insertion theorem and localic Tietze extension theorem
In this paper, localic upper, respectively lower continuous chains over a locale are defined. A localic Katětov-Tong insertion theorem is given and proved in terms of a localic upper and lower continuous chain. Finally, the localic Urysohn lemma and the localic Tietze extension theorem are shown as applications of the localic insertion theorem.
Locally admissible multi-valued maps
In this paper we generalize the class of admissible mappings as due by L. Górniewicz in 1976. Namely we define the notion of locally admissible mappings. Some properties and applications to the fixed point problem are presented.
Locally closed sets and LC-continuous functions.
Locally compact spaces C-tame at infinity.