Metrizable TAP, HTAP and STAP groups

Details Metrizable TAP, HTAP and STAP groups Metrizable TAP, HTAP and STAP groups

2009-09-08

arxiv.org/abs/0909.1400v2

Mathematics

General Topology

Scientific paper

In a recent paper by D. Shakhmatov and J. Sp\v{e}v\'ak [Group-valued continuous functions with the topology of pointwise convergence, Topology and its Applications (2009), doi:10.1016/j.topol.2009.06.022] the concept of a ${\rm TAP}$ group is introduced and it is shown in particular that ${\rm NSS}$ groups are ${\rm TAP}$. We prove that conversely, Weil complete metrizable ${\rm TAP}$ groups are ${\rm NSS}$. We define also the narrower class of ${\rm STAP}$ groups, show that the ${\rm NSS}$ groups are in fact ${\rm STAP}$ and that the converse statement is true in metrizable case. A remarkable characterization of pseudocompact spaces obtained in the paper by D. Shakhmatov and J. Sp\v{e}v\'ak asserts: a Tychonoff space $X$ is pseudocompact if and only if $C_p(X,\mathbb R)$ has the ${\rm TAP}$ property. We show that for no infinite Tychonoff space $X$, the group $C_p(X,\mathbb R)$ has the ${\rm STAP}$ property. We also show that a metrizable locally balanced topological vector group is ${\rm STAP}$ iff it does not contain a subgroup topologically isomorphic to $\mathbb Z^{(\mathbb N)}$.

Affiliated with

Also associated with

No associations

Rating

Metrizable TAP, HTAP and STAP groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Metrizable TAP, HTAP and STAP groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Metrizable TAP, HTAP and STAP groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-107764