Related papers: A separable non-remainder of H

We prove that the discontinuity group of every locally bounded homomorphism of a Lie group into a Lie group is not only compact and connected, which is known, but is also commutative.

We investigate dense lineability and spaceability of subsets of $\ell_\infty$ with a prescribed number of accumulation points. We prove that the set of all bounded sequences with exactly countably many accumulation points is densely…

We prove under ZFC that in each extremally disconnected compact space there exists a non-limit point of any countable discrete subset.

We show a number of undecidable assertions concerning countably compact spaces hold under PFA(S)[S]. We also show the consistency without large cardinals of "every locally compact, perfectly normal space is paracompact".

The main result of this article is: THEOREM. Every homogeneous locally conical connected separable metric space that is not a $1$-manifold is strongly $n$-homogeneous for each $n \geq 2$ and countable dense homogeneous. Furthermore,…

Let $p$ be a large prime, and let $k\ll \log p$. A new proof of the existence of any pattern of $k$ consecutive quadratic residues and quadratic nonresidues is introduced in this note. Further, an application to the least quadratic…

Let $X$ be a compact metric space and $\mathcal M_X$ be the set of isometry classes of compact metric spaces $Y$ such that the Lipschitz distance $d_L(X,Y)$ is finite. We show that $(\mathcal M_X, d_L)$ is not separable when $X$ is a closed…

In various places in the literature it is stated that every separable linear order embeds into the real line. This is, however, not the case, at least not with respect to the usual definition of separability. We correct this misconception.

We show that there are compact plane sets $X$, $Y$ such that $R(X)$ and $R(Y)$ are regular but $R(X \cup Y)$ is not regular.

We construct holomorphic maps with a Siegel disk whose boundary is not locally connected (and is an indecomposable continuum), yet compactly contained in the domain of definition of the map. Our examples are injective and defined on a…

Using elementary pcf, we show that there is no $j:V\to M,$ $M$ transitive, $j\lambda =\lambda >crit(j),$ $j^{\prime \prime}\lambda \in M.$

We provide examples of nonseparable compact spaces with the property that any continuous image which is homeomorphic to a finite product of spaces has a maximal prescribed number of nonseparable factors.

We shall prove that if X, Y are compact metrizable spaces of positive dimension and h: X x Y --> X is a continuous map with zero-dimensional fibers then X contains a non-trivial continuum without one-dimensional subsets; in particular X is…

In this work, we investigate compact K\"ahler manifolds with non-negative or quasi-positive mixed curvature coming from a linear combination of the Ricci and holomorphic sectional curvature, which covers various notions of curvature…

We show that the set $SCL^{rp}$ of stable commutator lengths on recursively presented groups equals the set of non-negative right-computable numbers. Hence all non-negative algebraic or computable numbers are in $SCL^{rp}$ and $SCL^{rp}$ is…

We prove that an infinitesimally Hilbertian CD(0,N) space containing a line splits as the product of $R$ and an infinitesimally Hilbertian CD(0,N-1) space. By `infinitesimally Hilbertian' we mean that the Sobolev space $W^{1,2}(X,d,m)$,…

We construct a compact nonpositively curved squared 2-complex whose universal cover contains a flat plane that is not the limit of periodic flat planes.

We show that locally connected, simply connected homogeneous continua are not separated by arcs. We ask several questions about homogeneous continua which are inspired by analogous questions in geometric group theory.

It is proved that the continuum hypothesis implies the existence of a group M containing a nonalgebraic unconditionally closed set, i.e., a set which is closed in any Hausdorff group topology on M but is not an intersection of finite unions…

In a recent paper \cite{T} the fact that a class of locally compact metric spaces $X$, among which are Euclidean spaces, are not homemorphic to their punctured version $X\men\{p\}$, was given an interesting new proof which does not use…