Monotone retracts of an arcwise connected continuum
Monotone union property in a class M of separable metric spaces
Monotone weak Lindelöfness
The definition of monotone weak Lindelöfness is similar to monotone versions of other covering properties: X is monotonically weakly Lindelöf if there is an operator r that assigns to every open cover U a family of open sets r(U) so that (1) ∪r(U) is dense in X, (2) r(U) refines U, and (3) r(U) refines r(V) whenever U refines V. Some examples and counterexamples of monotonically weakly Lindelöf spaces are given and some basic properties such as the behavior with respect to products and subspaces...
Monotonic mappings on ordered sets, a class of inequalities with finite differences and fixed points.
Monotonic mod one transformations
Monotonically normal -separable spaces may not be perfect
A topological space is said to be -separable if has a -closed-discrete dense subset. Recently, G. Gruenhage and D. Lutzer showed that -separable PIGO spaces are perfect and asked if -separable monotonically normal spaces are perfect in general. The main purpose of this article is to provide examples of -separable monotonically normal spaces which are not perfect. Extremely normal -separable spaces are shown to be stratifiable.
Monotonicity properties of some skew tent maps
Monotonous stability for neutral fixed points.
More about spaces with a small diagonal
Hušek defines a space X to have a small diagonal if each uncountable subset of X² disjoint from the diagonal has an uncountable subset whose closure is disjoint from the diagonal. Hušek proved that a compact space of weight ω₁ which has a small diagonal will be metrizable, but it remains an open problem to determine if the weight restriction is necessary. It has been shown to be consistent that each compact space with a small diagonal is metrizable; in particular, Juhász and Szentmiklóssy proved...
More Lusin properties in the product space
More on generalized homeomorphisms in topological spaces.
More on ordinals in topological groups
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...
More on rc-Lindelöf sets and almost rc-Lindelöf sets.
More on semi-Urysohn spaces.
More on sg-compact spaces.
More on strongly sequential spaces
Strongly sequential spaces were introduced and studied to solve a problem of Tanaka concerning the product of sequential topologies. In this paper, further properties of strongly sequential spaces are investigated.
More on the Kechris-Pestov-Todorcevic correspondence: Precompact expansions
In 2005, the paper [KPT05] by Kechris, Pestov and Todorcevic provided a powerful tool to compute an invariant of topological groups known as the universal minimal flow. This immediately led to an explicit representation of this invariant in many concrete cases. However, in some particular situations, the framework of [KPT05] does not allow one to perform the computation directly, but only after a slight modification of the original argument. The purpose of the present paper is to supplement [KPT05]...
More on the product of pseudo radial spaces
It is proved that the product of two pseudo radial compact spaces is pseudo radial provided that one of them is monolithic.
More on the shift dynamics-indecomposable continua connection.
More on tie-points and homeomorphism in ℕ*
A point x is a (bow) tie-point of a space X if X∖x can be partitioned into (relatively) clopen sets each with x in its closure. We denote this as where A, B are the closed sets which have a unique common accumulation point x. Tie-points have appeared in the construction of non-trivial autohomeomorphisms of βℕ = ℕ* (by Veličković and Shelah Steprans) and in the recent study (by Levy and Dow Techanie) of precisely 2-to-1 maps on ℕ*. In these cases the tie-points have been the unique fixed point...