All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2 Next

Displaying 21 – 40 of 41

Showing per page

On dense subspaces satisfying stronger separation axioms

Ofelia Teresa Alas, Mihail G. Tkachenko, Vladimir Vladimirovich Tkachuk, Richard Gordon Wilson, Ivan V. Yashchenko (2001)

Czechoslovak Mathematical Journal

We prove that it is independent of ZFC whether every Hausdorff countable space of weight less than c has a dense regular subspace. Examples are given of countable Hausdorff spaces of weight c which do not have dense Urysohn subspaces. We also construct an example of a countable Urysohn space, which has no dense completely Hausdorff subspace. On the other hand, we establish that every Hausdorff space of π -weight less than 𝔭 has a dense completely Hausdorff (and hence Urysohn) subspace. We show that...

On minimal Hausdorff and minimal Urysohn functions

Filippo Cammaroto, Andrei Catalioto, Jack Porter (2011)

Open Mathematics

In this article, we extend the work on minimal Hausdorff functions initiated by Cammaroto, Fedorchuk and Porter in a 1998 paper. Also, minimal Urysohn functions are introduced and developed. The properties of heredity and productivity are examined and developed for both minimal Hausdorff and minimal Urysohn functions.

On minimal strongly KC-spaces

Weihua Sun, Yuming Xu, Ning Li (2009)

Czechoslovak Mathematical Journal

In this article we introduce the notion of strongly KC -spaces, that is, those spaces in which countably compact subsets are closed. We find they have good properties. We prove that a space ( X , τ ) is maximal countably compact if and only if it is minimal strongly KC , and apply this result to study some properties of minimal strongly KC -spaces, some of which are not possessed by minimal KC -spaces. We also give a positive answer to a question proposed by O. T. Alas and R. G. Wilson, who asked whether every...

On minimal- α -spaces

Giovanni Lo Faro, Giorgio Nordo, Jack R. Porter (2003)

Commentationes Mathematicae Universitatis Carolinae

An α -space is a topological space in which the topology is generated by the family of all α -sets (see [N]). In this paper, minimal- α 𝒫 -spaces (where 𝒫 denotes several separation axioms) are investigated. Some new characterizations of α -spaces are also obtained.

On p -closed spaces.

Dontchev, Julian, Ganster, Maximilian, Noiri, Takashi (2000)

International Journal of Mathematics and Mathematical Sciences

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 .

Currently displaying 21 – 40 of 41