A minimalization of 0-dimensional metric spaces
A note on strong compactness and S-closedness
A unified theory of weak separation properties.
An independency result in connectification theory
A space is called connectifiable if it can be densely embedded in a connected Hausdorff space. Let be the following statement: “a perfect -space with no more than clopen subsets is connectifiable if and only if no proper nonempty clopen subset of is feebly compact". In this note we show that neither nor is provable in ZFC.
-compactness modulo an ideal.
Categories of topological spaces with sufficiently many sequentially closed spaces
Characterizations of Urysohn-closed spaces
Compact and extremally disconnected spaces.
Completely regular proximities and RC-proximities
Concerning almost realcompactifications
Diagonals and discrete subsets of squares
In 2008 Juhász and Szentmiklóssy established that for every compact space there exists a discrete with . We generalize this result in two directions: the first one is to prove that the same holds for any Lindelöf -space and hence is -separable. We give an example of a countably compact space such that is not -separable. On the other hand, we show that for any Lindelöf -space there exists a discrete subset such that ; in particular, the diagonal is a retract of and the projection...
Extending maps from dense subspaces .
Further remarks on KC and related spaces
A topological space is KC when every compact set is closed and SC when every convergent sequence together with its limit is closed. We present a complete description of KC-closed, SC-closed and SC minimal spaces. We also discuss the behaviour of the finite derived set property in these classes.
H-abgeschlossene Räume als schwach-stetige Bilder kompakter Räume.
H-closed functions
The notion of a Hausdorff function is generalized to the concept of H-closed function and the concept of an H-closed extension of a Hausdorff function is developed. Each Hausdorff function is shown to have an H-closed extension.
H-closed Spaces and Reflective Subcategories.
Minimal class generated by open compact and perfect mappings
Minimal realcompact spaces
Minimal sequential Hausdorff spaces.
-sets and near compact spaces
Si provano nuovi risultati riguardanti gli «-sets» e gli spazi «Near-compact». Si completano alcune ricerche pubblicate dai primi due autori nel 1978 e si risolvono due problemi recentemente posti da Cammaroto, Gutierrez, Nordo e Prada.