$\varepsilon $-mappings onto polyhedra

Transverse Cellular Mappings of Polyhedra

We generalize Marshall Cohen's notion of transverse cellular map to the polyhedral category. They are described by the following: Proposition. Let f : K —* L be a proper simplicial map of locally finite simplicial complexes. The following are equivalent: (1) The dual cells of the map are all cones. (2) The dual cells of the map are homogeneously collapsible in K. (3) The inclusion of L into the...

Quasilinear Mappings, M–ideals and Polyhedra

We survey the connection between two results from rather different areas: failure of the 3-space property for local convexity (and other properties) within the category of quasiBanach spaces, and the irreducibility (in the sense of Minkowski difference) of large families of finite dimensional polytopes. Mathematics subject classification (2010): 46A16, 46B03, 52B15..

Mappings of the Sierpinski Curve onto Itself

Given two points p and q of the Sierpinski universal plane curve S, necessary and/ or sufficient conditions are discussed in the paper under which there is a mapping I of S onto itself such that I(P) = q and I belongs to one of the following: homeomorphisms, local homeomorphisms, local homeomorphisms in the large sense, open, simple or monotone mappings.

On Lipschitz Mappings Onto a Square

Hereditarily Weakly Confluent Mappings onto S

Results are obtained about the existence and behavior of hereditarily weakly confluent maps of continua onto the unit circle S1. A simple and useful necessary and sufficient condition is given for a map of a continuum, X, onto S1 to be hereditarily weakly confluent (HWC). It is shown that when X is arcwise connected, an HWC map of X onto S1 is monotone with arcwise connected fibers. A number of...