Topology Proceedings UNIVERSAL LOCALLY COMPACT SCATTERED SPACES

One-point extensions of locally compact paracompact spaces

A space $Y$ is called an {em extension} of a space $X$, if $Y$ contains $X$ as a dense subspace. Two extensions of $X$ are said to be {em equivalent}, if there is a homeomorphism between them which fixes $X$ point-wise. For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Yleq Y'$, if there is a continuous function of $Y'$ into $Y$ which fixes $X$ point-wise. An extension $Y$ ...

Strongly k-spaces

‎In this paper‎, ‎we introduce the notion of strongly $k-$spaces (with the weak (=finest) pre-topology generated by their strongly compact subsets)‎. ‎We characterize the strongly $k-$spaces and investigate the relationships between preclosedness‎, ‎locally strongly compactness‎, ‎pre-first countableness and being strongly $k-$space.

Topology Proceedings 9 (1984) pp. 297-306: TWO NORMAL LOCALLY COMPACT SPACES UNDER MARTIN'S AXIOM

Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups

We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...

Universal Properties of Group Actions on Locally Compact Spaces

We study universal properties of locally compact G-spaces for countable infinite groups G. In particular we consider open invariant subsets of the G-space βG, and their minimal closed invariant subspaces. These are locally compact free G-spaces, and the latter are also minimal. We examine the properties of these G-spaces with emphasis on their universal properties. As an example of our results,...