Paracompacité et espaces uniformes
Paracompact box products in forcing extensions
Paracompactness and the Lindelöf property in finite and countable cartesian products
Paracompactness in box products
Paracompactness in countable products via the Souslin operation
Paracompactness in ordered spaces
Paracompactness in the class of closed images of GO-spaces
Paracompactness of topological completions
Paracompactness with respect to an ideal.
Partial discretization of topologies
In questo lavoro daremo una construzione che aumenta il numero di sottospazi chiusi e discreti dello spazio e daremo alcune applicazioni di tale construzione.
Partition continue de l'unite et C-repletion.
Partitions of compact Hausdorff spaces
Under the assumption that the real line cannot be covered by -many nowhere dense sets, it is shown that (a) no Čech-complete space can be partitioned into -many closed nowhere dense sets; (b) no Hausdorff continuum can be partitioned into -many closed sets; and (c) no compact Hausdorff space can be partitioned into -many closed -sets.
Peano compactifications and property S metric spaces.
Peculiar behavior of connected locales
P-embedding and product spaces
Perfect compactifications of frames
Perfect compactifications of frames are introduced. It is shown that the Stone-Čech compactification is an example of such a compactification. We also introduce rim-compact frames and for such frames we define its Freudenthal compactification, another example of a perfect compactification. The remainder of a rim-compact frame in its Freudenthal compactification is shown to be zero-dimensional. It is shown that with the assumption of the Boolean Ultrafilter Theorem the Freudenthal compactification...
Perfect compactifications of functions
We prove that the maximal Hausdorff compactification of a -compactifiable mapping and the maximal Tychonoff compactification of a Tychonoff mapping (see [P]) are perfect. This allows us to give a characterization of all perfect Hausdorff (respectively, all perfect Tychonoff) compactifications of a -compactifiable (respectively, of a Tychonoff) mapping, which is a generalization of two results of Skljarenko [S] for the Hausdorff compactifications of Tychonoff spaces.
Perfect mappings in topological groups, cross-complementary subsets and quotients
The following general question is considered. Suppose that is a topological group, and , are subspaces of such that . Under these general assumptions, how are the properties of and related to the properties of ? For example, it is observed that if is closed metrizable and is compact, then is a paracompact -space. Furthermore, if is closed and first countable, is a first countable compactum, and , then is also metrizable. Several other results of this kind are obtained....
Perfect maps in compact (countably compact) spaces.
Perfect pre-images of cofinally complete metric spaces
We show that a Tychonoff space is the perfect pre-image of a cofinally complete metric space if and only if it is paracompact and cofinally Čech complete. Further properties of these spaces are discussed. In particular, cofinal Čech completeness is preserved both by perfect mappings and by continuous open mappings.