The present paper aims to furnish simple proofs of some recent results about selections on product spaces obtained by Garcia-Ferreira, Miyazaki and Nogura. The topic is discussed in the framework of… Expand

Inspired by the fact that a compact topological group is hereditarily normal if and only if it is metrizable, we prove that various levels of compactness-like properties imposed on a topological… Expand

We show that if a topological or paratopological group $G$ contains a stationary subset of some regular uncountable cardinal, then $G$ contains a subspace which is not collectionwise normal. This… Expand

We work towards establishing that if it is consistent that there is a supercompact cardinal then it is consistent that every locally compact perfectly normal space is paracompact. At a crucial step… Expand

AbstractTopological properties similar to normality are considered in subspaces of products and powers of topological spaces, of spaces of closed subsets, and of spaces having the form … Expand

A topological space is nonseparably connected if it is connected but all of its connected separable subspaces are singletons. We show that each connected sequential topological space X is the image… Expand

We introduce and study the notion of pairwise monotonically normal space as a bitopological extension of the monotonically normal spaces of Heath, Lutzer and Zenor. In particular, we characterize… Expand

Although traditional and idempotent mathematics are "parallel'', by an application of the category theory we show that objects obtained the similar rules over traditional and idempotent mathematics… Expand