In this paper, we study the monotone meta-Lindelöf property. Relationships between monotone meta-Lindelöf spaces and other spaces are investigated. Behaviors of monotone meta-Lindelöf -spaces in their linearly ordered extensions are revealed.
Let be an uncountable regular cardinal and a topological group. We prove the following statements: (1) If is homeomorphic to a closed subspace of , is Abelian, and the order of every non-neutral element of is greater than then embeds in as a closed subspace. (2) If is Abelian, algebraically generated by , and the order of every element does not exceed then is not embeddable in . (3) There exists an Abelian topological group such that is homeomorphic to a closed subspace...
We provide a necessary and sufficient condition under which a generalized ordered topological product (GOTP) of two GO-spaces is monotonically Lindelöf.
We say that a real normed lattice is quasi-Baire if the intersection of each sequence of monotonic open dense sets is dense. An example of a Baire-convex space, due to M. Valdivia, which is not quasi-Baire is given. We obtain that is a quasi-Baire space iff , is a pairwise Baire bitopological space, where , is a quasi-uniformity that determines, in . Nachbin’s sense, the topological ordered space .
A scadic space is a Hausdorff continuous image of a product of compact scattered spaces. We complete a theorem begun by G. Chertanov that will establish that for each scadic space X, χ(X) = w(X). A ξ-adic space is a Hausdorff continuous image of a product of compact ordinal spaces. We introduce an either-or chain condition called Property which we show is satisfied by all ξ-adic spaces. Whereas Property is productive, we show that a weaker (but more natural) Property is not productive. Polyadic...
We call a function P-preserving if, for every subspace with property P, its image also has property P. Of course, all continuous maps are both compactness- and connectedness-preserving and the natural question about when the converse of this holds, i.e. under what conditions such a map is continuous, has a long history. Our main result is that any nontrivial product function, i.e. one having at least two nonconstant factors, that has connected domain, range, and is connectedness-preserving...