A positional characterization of the (n-1)-dimensional Sierpiński curve in (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 to be X ∩ M with topology generated by . Suppose is homeomorphic to the irrationals; must ? We have partial results. We also answer a question of Gruenhage by showing that if is homeomorphic to the “Long Cantor Set”, then .
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 (resp., ) 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.