The domain (δ) of a closed ∗-derivation δ in C(K) (K : a compact Hausdorff space) is a generalization of the space C(1)[0,1] of differentiable functions on [0,1]. In this paper, a problem proposed by Jarosz (1985) is studied in the context of derivations instead of C(1)[0,1].

We give several partial positive answers to a question of Juhász and Szentmiklóssy regarding the minimum number of discrete sets required to cover a compact space. We study the relationship between the size of discrete sets, free sequences and their closures with the cardinality of a Hausdorff space, improving known results in the literature.

It is shown that all compactifications of the positive integers N which have metrizable remainders are themselves metrizable. This is done by first proving that each Hausdorff compactification of a noncompact locally compact space is the graph closure in an appropriate space. It is then shown that any two compactifications of N which have homeomorphic metrizable remainders are homeomorphic.

We show that the space of all Lelek fans in a Cantor fan, equipped with the Hausdorff metric, is homeomorphic to the separable Hilbert space. This result is a special case of a general theorem we prove about spaces of upper semicontinuous functions on compact metric spaces that are strongly discontinuous.

Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...

We study properties of metric segments in the class all spaces considered up to an isometry, endowed with Gromov--Hausdorff distance. On isometry classes compact spaces, Gromov-Hausdorff distance is a metric. A segment that consists points lying between two given ones. By von Neumann--Bernays--Godel (NBG) axiomatic set theory, proper monster collection, e.g., collection cardinal sets. prove any...

We initiate a study of topological orthoalgebras (TOAs), concentrating on the compact case. Examples of TOAs include topological orthomodular lattices, and also the projection lattice of a Hilbert space. As the latter example illustrates, a lattice-ordered TOA need not be a topological lattice. However, we show that a compact Boolean TOA is a topological Boolean algebra. Using this, we prove th...

We show that for any co-amenable compact quantum group A = C(G) there exists a unique compact Hausdorff topology on the set EA(G) of isomorphism classes of ergodic actions of G such that the following holds: for any continuous field of ergodic actions of G over a locally compact Hausdorff space T the map T → EA(G) sending each t in T to the isomorphism class of the fibre at t is continuous if a...

Already in his PhD Thesis on compact Abelian semigropups under the direction of Karl Heinrich Hofmann the author was lead to investigate locally compact cones [18]. This happened in the setting of Hausdorff topologies. The theme of topological cones has been reappearing in the author’s work in a non-Hausdorff setting motivated by the needs of mathematical models for a denotational semantics of ...