A note on pseudocompact spaces and $k\sb{R}$-spaces

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Pseudocompact Spaces

Maximal pseudocompact spaces

Maximal pseudocompact spaces (i.e. pseudocompact spaces possessing no strictly stronger pseudocompact topology) are characterized. It is shown that submaximal pseudocompact spaces whose pseudocompact subspaces are closed need not be maximal pseudocompact. Various techniques for constructing maximal pseudocompact spaces are described. Maximal pseudocompactness is compared to maximal feeble compa...

A note on Volterra and Baire spaces

 In Proposition 2.6 in (G‎. ‎Gruenhage‎, ‎A‎. ‎Lutzer‎, ‎Baire and Volterra spaces‎, ‎textit{Proc‎. ‎Amer‎. ‎Math‎. ‎Soc.} {128} (2000)‎, ‎no‎. ‎10‎, ‎3115--3124) a condition that‎ ‎every point of $D$ is $G_delta$ in $X$ was overlooked‎. ‎So we‎ ‎proved some conditions by which a Baire space is equivalent to a‎ ‎Volterra space‎. ‎In this note we show that if $X$ is a‎ ‎monotonically normal $T_1...

A note on soft topological spaces

This paper demonstrates the redundancies concerning the increasing popular ``soft set" approaches to general topologies. It is shown that there is a complement preserving isomorphism (preserving arbitrary $widetilde{bigcup}$ and arbitrary $widetilde{bigcap}$) between the lattice ($mathcal{ST}_E(X,E),widetilde{subset}$) of all soft sets on $X$ with the whole parameter set $E$ as domains and the ...