A characterization of movable compacta.
A characterization of open mapping in terms of convergent sequences.
A characterization of paracompactness
A characterization of point semiuniformities.
A characterization of pseudocompactness.
A characterization of realcompactness in terms of the topology of pointwise convergence on the function space
A characterization of regular averaging operators and its consequences
We present a characterization of continuous surjections, between compact metric spaces, admitting a regular averaging operator. Among its consequences, concrete continuous surjections from the Cantor set 𝓒 to [0,1] admitting regular averaging operators are exhibited. Moreover we show that the set of this type of continuous surjections from 𝓒 to [0,1] is dense in the supremum norm in the set of all continuous surjections. The non-metrizable case is also investigated. As a consequence, we obtain...
A characterization of regular fuzzy spaces
A characterization of smoothness in dendroids
A characterization of strong inductive dimension
A characterization of the arc by means of the C-index of itssemigroup.
A characterization of the -realcompact space
A characterization of the meager ideal
We give a classical proof of the theorem stating that the -ideal of meager sets is the unique -ideal on a Polish group, generated by closed sets which is invariant under translations and ergodic.
A Characterization of the Sphere and Euclidean Space by Transformation Groups.
A characterization of topologically complete spaces in the sense of E. Čech in terms of convergence of functions
A characterization of unicoherence in terms of separating open sets
A characterization of Valdivia compact spaces.
A characterization of ω-limit sets for piecewise monotone maps of the interval
For a piecewise monotone map f on a compact interval I, we characterize the ω-limit sets that are bounded away from the post-critical points of f. If the pre-critical points of f are dense, for example when f is locally eventually onto, and Λ ⊂ I is closed, invariant and contains no post-critical point, then Λ is the ω-limit set of a point in I if and only if Λ is internally chain transitive in the sense of Hirsch, Smith and Zhao; the proof relies upon symbolic dynamics. By identifying points of...
A C(K) Banach space which does not have the Schroeder-Bernstein property
We construct a totally disconnected compact Hausdorff space K₊ which has clopen subsets K₊” ⊆ K₊’ ⊆ K₊ such that K₊” is homeomorphic to K₊ and hence C(K₊”) is isometric as a Banach space to C(K₊) but C(K₊’) is not isomorphic to C(K₊). This gives two nonisomorphic Banach spaces (necessarily nonseparable) of the form C(K) which are isomorphic to complemented subspaces of each other (even in the above strong isometric sense), providing a solution to the Schroeder-Bernstein problem for Banach spaces...
A Class of C*-Algebras and Topological Markov Chains.