Hopfian and strongly hopfian manifolds

Young Im; Yongkuk Kim

Displaying similar documents to “Hopfian and strongly hopfian manifolds”

A Lefschetz-type coincidence theorem

Peter Saveliev (1999)

Fundamenta Mathematicae

Similarity:

A Lefschetz-type coincidence theorem for two maps f,g: X → Y from an arbitrary topological space to a manifold is given: $I_{f g} = λ_{f g}$ , that is, the coincidence index is equal to the Lefschetz number. It follows that if $λ_{f g} \neq 0$ then there is an x ∈ X such that f(x) = g(x). In particular, the theorem contains well-known coincidence results for (i) X,Y manifolds, f boundary-preserving, and (ii) Y Euclidean, f with acyclic fibres. It also implies certain fixed point results for multivalued maps with “point-like”...

Loop spaces and homotopy operations

David Blanc (1997)

Fundamenta Mathematicae

Similarity:

We describe an obstruction theory for an H-space X to be a loop space, in terms of higher homotopy operations taking values in $π_{*} X$ . These depend on first algebraically “delooping” the Π-algebras $π_{*} X$ , using the H-space structure on X, and then trying to realize the delooped Π-algebra.

Filters and sequences

Sławomir Solecki (2000)

Fundamenta Mathematicae

Similarity:

We consider two situations which relate properties of filters with properties of the limit operators with respect to these filters. In the first one, we show that the space of sequences having limits with respect to a $Π_{3}^{0}$ filter is itself $Π_{3}^{0}$ and therefore, by a result of Dobrowolski and Marciszewski, such spaces are topologically indistinguishable. This answers a question of Dobrowolski and Marciszewski. In the second one, we characterize universally measurable filters which fulfill Fatou’s...

The minimum uniform compactification of a metric space

R. Grant Woods (1995)

Fundamenta Mathematicae

Similarity:

It is shown that associated with each metric space (X,d) there is a compactification $u_{d} X$ of X that can be characterized as the smallest compactification of X to which each bounded uniformly continuous real-valued continuous function with domain X can be extended. Other characterizations of $u_{d} X$ are presented, and a detailed study of the structure of $u_{d} X$ is undertaken. This culminates in a topological characterization of the outgrowth $u_{d} ℝ^{n} ∖ ℝ^{n}$ , where $(ℝ^{n}, d)$ is Euclidean n-space with its usual metric. ...

Some diophantine equations of the form $x^{n} + y^{n} = z^{m}$

Bjorn Poonen (1998)

Acta Arithmetica

Similarity:

Sums of fifth powers and related topics

Koichi Kawada, Trevor D. Wooley (1998)

Acta Arithmetica

Similarity:

Countable Toronto spaces

Gary Gruenhage, J. Moore (2000)

Fundamenta Mathematicae

Similarity:

A space X is called an α-Toronto space if X is scattered of Cantor-Bendixson rank α and is homeomorphic to each of its subspaces of the same rank. We answer a question of Steprāns by constructing a countable α-Toronto space for each α ≤ ω. We also construct consistent examples of countable α-Toronto spaces for each $α < ω_{1}$ .

Cantor manifolds in the theory of transfinite dimension

Wojciech Olszewski (1994)

Fundamenta Mathematicae

Similarity:

For every countable non-limit ordinal α we construct an α-dimensional Cantor ind-manifold, i.e., a compact metrizable space $Z_{α}$ such that $i n d Z_{α} = α$ , and no closed subset L of $Z_{α}$ with ind L less than the predecessor of α is a partition in $Z_{α}$ . An α-dimensional Cantor Ind-manifold can be constructed similarly.

Extending real-valued functions in βκ

Alan Dow (1997)

Fundamenta Mathematicae

Similarity:

An Open Coloring Axiom type principle is formulated for uncountable cardinals and is shown to be a consequence of the Proper Forcing Axiom. Several applications are found. We also study dense C*-embedded subspaces of ω*, showing that there can be such sets of cardinality $c$ and that it is consistent that ω*{pis C*-embedded for some but not all p ∈ ω*.

Classification of function spaces with the pointwise topology determined by a countable dense set

Tadeusz Dobrowolski, Witold Marciszewski (1995)

Fundamenta Mathematicae

Similarity:

PCA sets and convexity

R. Kaufman (2000)

Fundamenta Mathematicae

Similarity:

Three sets occurring in functional analysis are shown to be of class PCA (also called $Σ_{2}^{1}$ ) and to be exactly of that class. The definition of each set is close to the usual objects of modern analysis, but some subtlety causes the sets to have a greater complexity than expected. Recent work in a similar direction is in [1, 2, 10, 11, 12].

Linear orders and MA + ¬wKH

Zoran Spasojević (1995)

Fundamenta Mathematicae

Similarity:

I prove that the statement that “every linear order of size $2^{ω}$ can be embedded in $(ω^{ω}, ≪)$ ” is consistent with MA + ¬ wKH.

Products of shifted primes: Multiplicative analogues of Goldbach's problem

P. D. T. A. Elliott (1999)

Acta Arithmetica

Similarity:

The normalizer splitting conjecture for p-compact groups

Kasper Andersen (1999)

Fundamenta Mathematicae

Similarity:

Let X be a p-compact group, with maximal torus BT → BX, maximal torus normalizer BN and Weyl group $W_{X}$ . We prove that for an odd prime p, the fibration $B T \to B N \to B W_{X}$ has a section, which is unique up to vertical homotopy.