A Compact Homogeneous S-space

极端不连通空间乘积的齐次子空间

Homogeneous Subspaces of Products of Extremally Disconnected Spaces

该研究构造了乘积非伪紧的齐次可数紧空间，证明了极端不连通空间各次幂齐次子空间的紧子集相关性质，强化了Frolík定理。

Amalgams, connectifications, and homogeneous compacta

We construct a path-connected homogenous compactum with cellularity 2^omega that is not homeomorphic to any product of dyadic compacta and first countable compacta. We also prove some closure properties for classes of spaces defined by various connectifiability conditions. One application is that every infinite product of infinite topological sums of T_i spaces has a T_i pathwise connectification, where i is 1, 2, 3, or 3.5.

Homogeneity properties in large compact S-spaces

Under Jensen's Diamond Principle, we show how to construct a large compact S-space while having some control over its group of autohomeomorphisms. In particular we can make the space rigid or h-homogeneous (i.e. any two clopen subsets are homeomorphic). We also get a space which is B-homogeneous and not h-homogeneous, partially answering a question of M.V. Matveev. A space is B-homogeneous if it has a base every element of which can be mapped onto every other one by a homeomorphism of the whole space.

On the weak tightness, Hausdorff spaces, and power homogeneous compacta

Motivated by results of Juhász and van Mill in [13], we define the cardinal invariant $wt(X)$, the weak tightness of a topological space $X$, and show that $|X|\leq 2^{L(X)wt(X)ψ(X)}$ for any Hausdorff space $X$ (Theorem 2.8). As $wt(X)\leq t(X)$ for any space $X$, this generalizes the well-known cardinal inequality $|X|\leq 2^{L(X)t(X)ψ(X)}$ for Hausdorff spaces (Arhangel{\cprime}skiĭ~[1],Š}apirovskiĭ}~[18]) in a new direction. Theorem 2.8 is generalized further using covers by $G_κ$-sets, where $κ$ is a cardinal, to show that if $X$ is a power homogeneous compactum with a countable cover of …

齐性局部紧空间

Homogeneous locally compact spaces

本文综述局部紧齐性度量空间的最新结果与未解决问题，重点讨论齐性有限维ANR-空间。

Between homeomorphism type and Tukey type

Call a compact space $X$ pin homogeneous if every two points $a,b$ are pin equivalent, meaning that there exists a compact space $Y$, a quotient map $f\colon Y\to X$, and a homeomorphism $g\colon Y\to Y$ such that $gf^{-1}\{a\}=f^{-1}\{b\}$. We will prove a representation theorem for pin equivalence; transitivity of pin equivalence will be a corollary. Pin homogeneity is strictly weaker than homogeneity and pin equivalence is strictly stronger than Tukey equivalence. Just as with topological homogeneity, no infinite compact $F$-space is pin homogeneous. On the other hand, $X\times 2^{χ(X)}$ is…