An Egoroff-type theorem for set-valued measurable functions.
An elementary proof of Noble's theorem on normality of powers
An embedding theorem for semigroups of continuous selfmaps.
An embedding theorem of infinite-dimensional manifold pairs in the model space
An Equivariant Extension Theorem and G-Retracts with a Finite Structure.
An evaluating characterization of homomorphisms
This work provides an evaluating complete description of positive homomorphisms on an arbitrary algebra of real-valued functions.
An exact sequence from the nth to the (n-1)-st fundamental group
An Exactly Two-to-One Map from an Indecomposable Chainable Continuum
It is shown that a certain indecomposable chainable continuum is the domain of an exactly two-to-one continuous map. This answers a question of Jo W. Heath.
An example concerning automorphisms of generalized cubes
An example concerning the Whitehead Theorem in shape theory
An Example Concerning Valdivia Compact Spaces
∗ Supported by Research grants GAUK 190/96 and GAUK 1/1998We prove that the dual unit ball of the space C0 [0, ω1 ) endowed with the weak* topology is not a Valdivia compact. This answers a question posed to the author by V. Zizler and has several consequences. Namely, it yields an example of an affine continuous image of a convex Valdivia compact (in the weak* topology of a dual Banach space) which is not Valdivia, and shows that the property of the dual unit ball being Valdivia is not an isomorphic...
An example for mappings related to confluence
Confluence of a mapping between topological spaces can be defined by several ways. J.J. Charatonik asked if two definitions of the confluence using the components and quasi-components are equivalent for surjective mappings with compact point inverses. We give the negative answer to this question in Example 2.1.
An example for mappings related to semi-confluence.
An example in the theory of approximate systems
An approximate inverse sequence of plane continua is constructed which negatively answers a question of S. Mardeši’c related to approximate and usual inverse systems. The example also shows that an important result of M.G. Charalambous cannot be improved. As an application, it is shown that a procedure of making an approximate inverse sequence commutative (“taming”) is discontinuous.
An example of 2-dimensional quasihomeomorphic sets
An example of a genuinely discontinuous generically chaotic transformation of the interval
It is proved that a piecewise monotone transformation of the unit interval (with a countable number of pieces) is generically chaotic. The Gauss map arising in connection with the continued fraction expansions of the reals is an example of such a transformation.
An example of a group convergence with unique sequential limits which cannot be associated with a Hausdorff topology
An example of a monostratiform λ-dendroid
An example of a non-compact locally compact arcwise connected metric space with the fixed point property
An example of a probabilistic metric space not induced from a random normed space.