Topological volumes of fibrations: a note on open covers

A note on quasi irresolute topological groups

In this study, we investigate the further properties of quasi irresolute topological groups defined in [20]. We show that if a group homomorphism f between quasi irresolute topological groups is irresolute at $e_G$, then $f$ is irresolute on $G$. Later we prove that in a semi-connected quasi irresolute topological group $(G,*,tau )$, if $V$ is any symmetric semi-open neighborhood of $e_G$, then...

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 ...

A Note on Discrete Conduché Fibrations

The class of functors known as discrete Conduché fibrations forms a common generalization of discrete fibrations and discrete opfibrations, and shares many of the formal properties of these two classes. F. Lamarche [7] conjectured that, for any small category B, the category DCF/B of discrete Conduché fibrations over B should be a topos. In this note we show that, although for suitable categori...

Abelian Covers and Isotrivial Canonical Fibrations

We give a pure algebraic method to construct all the infinite families of surfaces S with isotrivial canonical fibration where S is the minimal desingularization of X = Z/G and G is an Abelian group acting diagonally on the product of two smooth curves: Z = F ×D. In particular we recover all the known infinite families of surfaces with isotrivial canonical fibration and we produce many new ones...

A Note on Range-Restricted Circuit Covers