A Theorem of the Closed Graph Type.
A theorem on coincidence point for a family of mappings.
A theorem on common fixed points of expansion type mappings in cone metric spaces.
A Theorem On Contraction Mappings
A theorem on contraction mappings.
A theorem on contractive mappings
A theorem on the common fixed point in locally convex spaces
A topological lattice on the set of multifunctions.
A topological representation of polarity lattices.
A topological representation of Post algebras and free Post algebras
A topological version of the Schauder theorem
A topology for automata. II.
A topology generated by eventually different functions
A unique common fixed point theorem for occasionally weakly compatible maps.
A Universal Proper G-Space.
A universal property of -semigroups
Let be a -semigroup with unbounded generator . We prove that has generically a very irregular behaviour for as .
A weakly chainable uniquely arcwise connected continuum without the fixed point property
A continuum is a metric compact connected space. A continuum is chainable if it is an inverse limit of arcs. A continuum is weakly chainable if it is a continuous image of a chainable continuum. A space X is uniquely arcwise connected if any two points in X are the endpoints of a unique arc in X. D. P. Bellamy asked whether if X is a weakly chainable uniquely arcwise connected continuum then every mapping f: X → X has a fixed point. We give a counterexample.
A -porous set need not be -bilaterally porous
A closed subset of the real line which is right porous but is not -left-porous is constructed.
AANR spaces and absolute retracts for tree-like continua
Continua that are approximative absolute neighborhood retracts (AANR’s) are characterized as absolute terminal retracts, i.e., retracts of continua in which they are embedded as terminal subcontinua. This implies that any AANR continuum has a dense arc component, and that any ANR continuum is an absolute terminal retract. It is proved that each absolute retract for any of the classes of: tree-like continua, -dendroids, dendroids, arc-like continua and arc-like -dendroids is an approximative absolute...
Abelian pro-countable groups and orbit equivalence relations
We study a class of abelian groups that can be defined as Polish pro-countable groups, as non-archimedean groups with a compatible two-sided invariant metric or as quasi-countable groups, i.e., closed subdirect products of countable discrete groups, endowed with the product topology. We show that for every non-locally compact, abelian quasi-countable group G there exists a closed L ≤ G and a closed, non-locally compact K ≤ G/L which is a direct product of discrete countable groups....