A short proof of Parovičenko's theorem
A simplified formula for calculation of metric dimension of converging sequences
A singular plane curve
A somewhat surprising subspace of
A study of universal elements in classes of bases of topological spaces
The universality problem focuses on finding universal spaces in classes of topological spaces. Moreover, in “Universal spaces and mappings” by S. D. Iliadis (2005), an important method of constructing such universal elements in classes of spaces is introduced and explained in details. Simultaneously, in “A topological dimension greater than or equal to the classical covering dimension” by D. N. Georgiou, A. C. Megaritis and F. Sereti (2017), new topological dimension is introduced and studied, which...
A subset theorem in dimension theory
A sum theorem for A-weakly infinite-dimensional spaces
A SURVEY OF SEMIGROUPS OF CONTINUOUS SELFMAPS.
A theorem on the weak topology of C(X) for compact scattered X
A theory of proper shape for locally compact metric spaces
A topological characterization of stationary sets
A topology with order, graph and an enumeration problem.
A transfinite extension of the covering dimension
A universal planar completely regular continuum
We construct a universal planar completely regular continuum. This gives a positive answer to a problem posed by J. Krasinkiewicz (1986).
A universal separable metric locally finite-dimensional space
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 wildly embedded 1-dimensional compact set in each of whose components is tame
A Z-set unknotting theorem for Nöbeling spaces
We prove a Z-set unknotting theorem for Nöbeling spaces.
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...
Absolute end points and their mapping properties.