Inverse invariance of metrizability for ordered spaces
I-weight of compact and locally compact LOTS
Ram’ırez-Páramo proved that under GCH for the class of compact Hausdorff spaces i-weight reflects all cardinals [A reflection theorem for i-weight, Topology Proc. 28 (2004), no. 1, 277–281]. We show that in ZFC i-weight reflects all cardinals for the class of compact LOTS. We define local i-weight, then calculate i-weight of locally compact LOTS and paracompact spaces in terms of the extent of the space and the i-weight of open sets or the local i-weight. For locally compact LOTS we find a necessary...
-spaces
In this paper -spaces are introduced and studied. They are a common generalization of Lindelöf spaces and -spaces researched by E. Michael. A space is called an -space if, whenever is a closed cover of with compact, then or is Lindelöf. Semi-strong -spaces and strong -spaces are also defined and investigated. It is demonstrated that the three spaces are different and have interesting properties and behaviors.
Large free set
Lattice of -compact topological spaces
Left translations of compact semilattices and generalizations
Left-separated spaces: a comment to a paper of M. G. Tkačenko
Linear and -linear betweenness spaces
Local connectivity and maps onto non-metrizable arcs.
Local convexity in topological lattices
Locally connected images of ordered compacta
Maximal Elements in Ordered Topological Spaces
Maximality principle and general results of Ekeland and Caristi types without lower semicontinuity assumptions in cone uniform spaces with generalized pseudodistances.
Measurability of Functions of Two Variables
Measure and measurable functions of
Metrizability of certain Pixley-Roy spaces
Metrizability of trees
Metrization of uniform lattices
Modifications of the double arrow space and related Banach spaces C(K)
We consider the class of compact spaces which are modifications of the well known double arrow space. The space is obtained from a closed subset K of the unit interval [0,1] by “splitting” points from a subset A ⊂ K. The class of all such spaces coincides with the class of separable linearly ordered compact spaces. We prove some results on the topological classification of spaces and on the isomorphic classification of the Banach spaces .
Monotone extenders for bounded c-valued functions
Let c be the Banach space consisting of all convergent sequences of reals with the sup-norm, the set of all bounded continuous functions f: A → c, and the set of all functions f: X → c which are continuous at each point of A ⊂ X. We show that a Tikhonov subspace A of a topological space X is strong Choquet in X if there exists a monotone extender . This shows that the monotone extension property for bounded c-valued functions can fail in GO-spaces, which provides a negative answer to a question...