Correction to "On real-valued functions in topological spaces"
On Real-Valued Functions in Topological Spaces
Complete normality of cartesian products
Measures in Fully Normal Spaces
On mapping of countable spaces
Remarks on Boolean algebras
Matematické metody v psychologii
Česká matematika v letech 1945-1985: topologie, teorie kategorií a kombinatorika
P. S. Uryson a počátky obecné topologie
N. N. Luzin a teorie reálných funkcí
О соотношении между метрической и топологической размерностью
On idempotent filters
Lineární operátory. II
O dvou výsledcích z obecné topologie
On -closed extensions of topological spaces
Entropies of self-mappings of topological spaces with richer structures
For mappings , where is a merotopic space equipped with a diameter function, we introduce and examine an entropy, called the -entropy. The topological entropy and the entropy of self-mappings of metric spaces are shown to be special cases of the -entropy. Some connections with other characteristics of self-mappings are considered. We also introduce and examine an entropy for subsets of , which is closely connected with the -entropy of .
Entropy-like functionals: conceptual background and some results
We describe a conceptual approach which provides a unified view of various entropy-like functionals on the class of semimetric spaces, endowed with a bounded measure. The entropy considered in the author’s previous articles is modified so as to assume finite values for a fairly wide class of spaces which fail to be totally bounded.
On entropy-like functionals and codes for metrized probability spaces II
In Part I, we have proved characterization theorems for entropy-like functionals , , , and restricted to the class consisting of all finite spaces , the class of all semimetric spaces equipped with a bounded measure. These theorems are now extended to the case of , and defined on the whole of , and of and restricted to a certain fairly wide subclass of .
An approach to covering dimensions
Using certain ideas connected with the entropy theory, several kinds of dimensions are introduced for arbitrary topological spaces. Their properties are examined, in particular, for normal spaces and quasi-discrete ones. One of the considered dimensions coincides, on these spaces, with the Čech-Lebesgue dimension and the height dimension of posets, respectively.
Extensions of the Shannon entropy to semimetrized measure spaces
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