51,514 research outputs found
Homogeneous Subspaces of Products of Extremally Disconnected Spaces
Homogeneous countably compact spaces and whose product is
not pseudocompact are constructed. It is proved that all compact subsets of
homogeneous subspaces of the third power of an extremally disconnected space
are finite. Moreover, under CH, all compact subsets of homogeneous subspaces of
any finite power of an extremally disconnected space are finite and all compact
subsets of homogeneous subspaces of the countable power of an extremally
disconnected space are metrizable. It is also proved that all compact
homogeneous subspaces of finite powers of an extremally disconnected space are
finite, which strengthens Frol\'{\i}k's theorem
Cardinal invariants for C-cross topologies
C-cross topologies are introduced. Modifcations of the Kuratowski-Ulam
Theorem are considered. Cardinal invariants add, cof, cov and non with respect
to meager or nowhere dense subsets are compared. Remarks on invariants
cof(nwdY) are mentioned for dense subspaces Y of X.Comment: 11 page
A general approach to Read's type constructions of operators without non-trivial invariant closed subspaces
We present a general method for constructing operators without non-trivial
invariant closed subsets on a large class of non-reflexive Banach spaces. In
particular, our approach unifies and generalizes several constructions due to
Read of operators without non-trivial invariant subspaces on the spaces
, or , and without non-trivial invariant
subsets on . We also investigate how far our methods can be extended
to the Hilbertian setting, and construct an operator on a quasireflexive dual
Banach space which has no non-trivial -closed invariant subspace.Comment: Minor modification
- …