Separating maps and the nonarchimedean Hewitt theorem
Separating sets by Darboux-like functions
We consider the following problem: Characterize the pairs ⟨A,B⟩ of subsets of ℝ which can be separated by a function from a given class, i.e., for which there exists a function f from that class such that f = 0 on A and f = 1 on B (the classical separation property) or f < 0 on A and f > 0 on B (a new separation property).
Sequential Cauchy spaces
Sequential completeness of subspaces of products of two cardinals
Let be a cardinal number with the usual order topology. We prove that all subspaces of are weakly sequentially complete and, as a corollary, all subspaces of are sequentially complete. Moreover we show that a subspace of need not be sequentially complete, but note that is sequentially complete whenever and are subspaces of .
Sequential continuity on dyadic compacta and topological groups
We study conditions under which sequentially continuous functions on topological spaces and sequentially continuous homomorphisms of topological groups are continuous.
Sequential convergence in
I discuss the number of iterations of the elementary sequential closure operation required to achieve the full sequential closure of a set in spaces of the form .
Sequentially complete spaces
Sequentially continuous mappings of product spaces
Sequentially quotient mappings
Set-set topologies and semitopological groups.
Set-valued mappings on metric spaces
Set-valued maps with fixed and coincidence points.
Several characterizations of SSDR-maps
Several classes of uniform spaces connected with Banach valued mappings
Several extremal coreflective classes in uniform spaces
s-Fibrations
Shape groups for -algebras.
Shape index in metric spaces
We extend the shape index, introduced by Robbin and Salamon and Mrozek, to locally defined maps in metric spaces. We show that this index is additive. Thus our construction answers in the affirmative two questions posed by Mrozek in [12]. We also prove that the shape index cannot be arbitrarily complicated: the shapes of q-adic solenoids appear as shape indices in natural modifications of Smale's horseshoes but there is not any compact isolated invariant set for any locally defined map in a locally...
Shape Invariant Functors: Application in Module-Theory.
Shape morphisms and spaces of approximative maps