A note on countable connected locally connected Urysohn almost regular spaces
A note on countable dense homogeneity
A note on countably determined and distinguishable sets
A note on cyclic subelement theory-reducibility of local connectedness and local simple connectedness
A note on dense subspaces of dyadic compact spaces
A note on diagonal and matrix properties of convergence 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 dimension theory of metric spaces
A note on discrete sets
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.
A note on discretely absolutely star-Lindelöf spaces
A note on D-spaces
Every semi-stratifiable space or strong -space has a -cushioned (mod)-network. In this paper it is showed that every space with a -cushioned (mod)-network is a D-space, which is a common generalization of some results about D-spaces.
A note on E-compact spaces
A note on embeddings manifolds into topological groups preserving dimensions
A note on exponentiation in regular locales
A note on extremally disconnected frames
A note on Fiedler-Moravek combinatorial problem
A note on Fixed Point Mappings with contracting orbital diameters.
A note on fixed point theorem of Schauder type with applications
A note on fixed points of a selfmap of an extremally disconnected space
A note on f.p.p. and
In [3], Kinoshita defined the notion of and he proved that each compact AR has In [4], Yonezawa gave some examples of not locally connected continua with f.p.p., but without In general, for each n=1,2,..., there is an n-dimensional continuum with f.p.p., but without such that is locally (n-2)-connected (see [4, Addendum]). In this note, we show that for each n-dimensional continuum X which is locally (n-1)-connected, X has f.p.p. if and only if X has