A hedgehog in a product
A hereditarily indecomposable non-metric Hausdorff continuum
A minimal regular ring extension of C(X)
Let G(X) denote the smallest (von Neumann) regular ring of real-valued functions with domain X that contains C(X), the ring of continuous real-valued functions on a Tikhonov topological space (X,τ). We investigate when G(X) coincides with the ring of continuous real-valued functions on the space , where is the smallest Tikhonov topology on X for which and is von Neumann regular. The compact and metric spaces for which are characterized. Necessary, and different sufficient, conditions...
A minimalization of 0-dimensional metric spaces
A nice subclass of functionally countable spaces
A space is functionally countable if is countable for any continuous function . We will call a space exponentially separable if for any countable family of closed subsets of , there exists a countable set such that whenever and . Every exponentially separable space is functionally countable; we will show that for some nice classes of spaces exponential separability coincides with functional countability. We will also establish that the class of exponentially separable spaces has...
A nondegenerate σ-discrete Moore space which is connected
A note on collectionwise normality and product spaces
A Note on Differentiability of Lipschitz Maps
We show that every Lipschitz map defined on an open subset of the Banach space C(K), where K is a scattered compactum, with values in a Banach space with the Radon-Nikodym property, has a point of Fréchet differentiability. This is a strengthening of the result of Lindenstrauss and Preiss who proved that for countable compacta. As a consequence of the above and a result of Arvanitakis we prove that Lipschitz functions on certain function spaces are Gâteaux differentiable.
A note on extremally disconnected frames
A note on fixed points of a selfmap of an extremally disconnected space
A note on Fréchet spaces
A note on maximally resolvable spaces.
A note on nowhere dense sets in
A note on P-spaces.
A note on Rudin's example of Dowker space
A note on separability of the Fell-hyperspace topology
A note on the algebraic de Morgan's law
A note on transitively -spaces
In this note, we show that if for any transitive neighborhood assignment for there is a point-countable refinement such that for any non-closed subset of there is some such that , then is transitively . As a corollary, if is a sequential space and has a point-countable -network then is transitively , and hence if is a Hausdorff -space and has a point-countable -network, then is transitively . We prove that if is a countably compact sequential space and has a point-countable...
A perfectly normal locally metrizable non-paracompact space
A rigid space admitting compact operators
A rigid space is a topological vector space whose endomorphisms are all simply scalar multiples of the identity map. The first complete rigid space was published in 1981 in [2]. Clearly a rigid space is a trivial-dual space, and admits no compact endomorphisms. In this paper a modification of the original construction results in a rigid space which is, however, the domain space of a compact operator, answering a question that was first raised soon after the existence of complete rigid spaces was...