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Some versions of relative paracompactness and their absolute embeddings

Shinji Kawaguchi (2007)

Commentationes Mathematicae Universitatis Carolinae

Arhangel’skii [Sci. Math. Jpn. 55 (2002), 153–201] defined notions of relative paracompactness in terms of locally finite open partial refinement and asked if one can generalize the notions above to the well known Michael’s criteria of paracompactness in [17] and [18]. In this paper, we consider some versions of relative paracompactness defined by locally finite (not necessarily open) partial refinement or locally finite closed partial refinement, and also consider closure-preserving cases, such...

Spaces in which compact subsets are closed and the lattice of $T_{1}$ -topologies on a set

Ofelia Teresa Alas, Richard Gordon Wilson (2002)

Commentationes Mathematicae Universitatis Carolinae

We obtain some new properties of the class of KC-spaces, that is, those topological spaces in which compact sets are closed. The results are used to generalize theorems of Anderson [1] and Steiner and Steiner [12] concerning complementation in the lattice of $T_{1}$ -topologies on a set $X$ .

Spaces with zero set bases

Michael L. Wage (1977)

Commentationes Mathematicae Universitatis Carolinae

Spaces $α$ - $s g$ - $T_{i}$ $i = 0, 1, 2, 3$ .

Rosas, Ennis (2003)

Divulgaciones Matemáticas

$Spec (R)$ and separation axioms between $T_{0}$ and $T_{1}$ .

Ávila G., Jesús Antonio (2005)

Divulgaciones Matemáticas

Strong sequences and the weight of regular spaces

Marian Turzański (1992)

Commentationes Mathematicae Universitatis Carolinae

It will be shown that if in a family of sets there exists a strong sequence of the length ${(κ^{λ})}^{+}$ then this family contains a subfamily consisting of $λ^{+}$ pairwise disjoint sets. The method of strong sequences will be used for estimating the weight of regular spaces.