We describe the extension of the multiplication on a not-necessarily-discrete topological monoid to its flow compactification. We offer two applications. The first is a nondiscrete version of Hindman’s Theorem, and the second is a characterization of the projective minimal and elementary flows in terms of idempotents of the flow compactification of the monoid.

In his paper "Continuous mappings on continua" [5], T. Maćkowiak collected results concerning mappings on metric continua. These results are theorems, counterexamples, and unsolved problems and are listed in a series of tables at the ends of chapters. It is the purpose of the present paper to provide solutions (three proofs and one example) to four of those problems.

“The kernel functor” $W\stackrel{k}{\to }LFrm$ from the category $W$ of archimedean lattice-ordered groups with distinguished weak unit onto LFrm, of Lindelöf completely regular frames, preserves and reflects monics. In $W$, monics are one-to-one, but not necessarily so in LFrm. An embedding $\varphi \in W$ for which $k\varphi$ is one-to-one is termed kernel-injective, or KI; these are the topic of this paper. The situation is contrasted with kernel-surjective and -preserving (KS and KP). The $W$-objects every embedding of which is KI are characterized;...

An example of two $M$-equivalent (hence $l$-equivalent) compact spaces is presented, one of which is Fréchet and the other is not.

A space Y is called a free space if for each compactum X the set of maps with hereditarily indecomposable fibers is a dense $G_{\delta }$-subset of C(X,Y), the space of all continuous functions of X to Y. Levin proved that the interval I and the real line ℝ are free. Krasinkiewicz independently proved that each n-dimensional manifold M (n ≥ 1) is free and the product of any space with a free space is free. He also raised a number of questions about the extent of the class of free spaces. In this paper we will...

In un progetto di generalizzazione delle classiche topologie di tipo «set-open» di Arens-Dugundji introduciamo un metodo generale per produrre topologie in spazi di funzioni mediante l'uso di ipertopologie. Siano $X$, $Y$ spazi topologici e $C\left(X,Y\right)$ l'insieme delle funzioni continue da $X$ verso $Y$. Fissato un «network» $\alpha$ nel dominio $X$ ed una topologia $\tau$ nell'iperspazio $CL\left(Y\right)$ del codominio $Y$ si genera una topologia ${\tau }_{\alpha }$ in $C\left(X,Y\right)$ richiedendo che una rete $\left\{f_{\lambda }\right\}$ di $C\left(X,Y\right)$ converge in ${\tau }_{\alpha }$ ad $f\in C\left(X,Y\right)$ se e solo se la rete $\left\{\overline{f_{\lambda }\left(A\right)}\right\}$ converge in $\tau$ ad $\overline{f\left(A\right)}$...

Necessary conditions and sufficient conditions are given for $C_p\left(X\right)$ to be a (σ-) m₁- or m₃-space. (A space is an m₁-space if each of its points has a closure-preserving local base.) A compact uncountable space K is given with $C_p\left(K\right)$ an m₁-space, which answers questions raised by Dow, Ramírez Martínez and Tkachuk (2010) and Tkachuk (2011).

We prove several stability properties for the class of compact Hausdorff spaces $T$ such that $C\left(T\right)$ with the weak or the pointwise topology is in the class of Stegall. In particular, this class is closed under arbitrary products.

We give a partial classification of spaces $C_p\left([1,\alpha ]\right)$ of continuous real valued functions on ordinals with the topology of pointwise convergence with respect to homeomorphisms and uniform homeomorphisms.

We apply the general theory of $\tau$-Corson Compact spaces to remove an unnecessary hypothesis of zero-dimensionality from a theorem on polyadic spaces of tightness $\tau$. In particular, we prove that polyadic spaces of countable tightness are Uniform Eberlein compact spaces.