### A positional characterization of the (n-1)-dimensional Sierpiński curve in ${S}^{n}$ (η ≠ 4)

### A property of the Sorgenfrey line

### A short proof of Parovičenko's theorem

### An extension theorem for sober spaces and the Goldman topology.

### An irrational problem

Given a topological space ⟨X,⟩ ∈ M, an elementary submodel of set theory, we define ${X}_{M}$ to be X ∩ M with topology generated by $U\cap M:U\in \cap M$. Suppose ${X}_{M}$ is homeomorphic to the irrationals; must $X={X}_{M}$? We have partial results. We also answer a question of Gruenhage by showing that if ${X}_{M}$ is homeomorphic to the “Long Cantor Set”, then $X={X}_{M}$.

### Borel sets in compact spaces: some Hurewicz type theorems

### Caractérisation topologique de l'espace des fonctions dérivables

### Characterization of Hilbert cube manifolds: an alternate proof

### Characterizations of the countable infinite product of rationals and some related problems

### Characterizing the interval and circle by composition of functions

### Classical-type characterizations of non-metrizable ANE(n)-spaces

The Kuratowski-Dugundji theorem that a metrizable space is an absolute (neighborhood) extensor in dimension n iff it is $L{C}^{n-1}{C}^{n-1}$ (resp., $L{C}^{n-1}$) is extended to a class of non-metrizable absolute (neighborhood) extensors in dimension n. On this base, several facts concerning metrizable extensors are established for non-metrizable ones.

### Closed copies of the rationals

### Compact spaces homeomorphic to a ray of ordinals

### Compacta which are quasi-homeomorphic with a disk

### Construction of a Hurewicz metric space whose square is not a Hurewicz space

### Continua determined by mappings.

### Continuous decompositions of Peano plane continua into pseudo-arcs

Locally planar Peano continua admitting continuous decomposition into pseudo-arcs (into acyclic curves) are characterized as those with no local separating point. This extends the well-known result of Lewis and Walsh on a continuous decomposition of the plane into pseudo-arcs.

### Every graph is a self-similar set.

### External Characterization of I-Favorable Spaces

1991 AMS Math. Subj. Class.:Primary 54C10; Secondary 54F65We provide both a spectral and an internal characterizations of arbitrary !-favorable spaces with respect to co-zero sets. As a corollary we establish that any product of compact !-favorable spaces with respect to co-zero sets is also !-favorable with respect to co-zero sets. We also prove that every C* -embedded !-favorable with respect to co-zero sets subspace of an extremally disconnected space is extremally disconnected.