A characterization of locally connected continua which are quasi-embeddable into
A class α and locally connected continua which can be ε-mapped onto a surface
A Cone of Inhomogeneous Second-Order Polynomials.
A note on realcompact unions
A proof for the Blair-Hager-Johnson theorem on absolute -embedding
In this paper, a simple proof is given for the following theorem due to Blair [7], Blair-Hager [8] and Hager-Johnson [12]: A Tychonoff space is -embedded in every larger Tychonoff space if and only if is almost compact or Lindelöf. We also give a simple proof of a recent theorem of Bella-Yaschenko [6] on absolute embeddings.
A remark on the weak topology of the Hilbert space
A universal planar completely regular continuum
We construct a universal planar completely regular continuum. This gives a positive answer to a problem posed by J. Krasinkiewicz (1986).
A universal separable metric locally finite-dimensional space
An example related to strongly pointwise self-homeomorphic dendrites
Such spaces in which a homeomorphic image of the whole space can be found in every open set are called self-homeomorphic. W.J. Charatonik and A. Dilks posed a problem related to strongly pointwise self-homeomorphic dendrites. We solve this problem negatively in Example 2.1.
An independency result in connectification theory
A space is called connectifiable if it can be densely embedded in a connected Hausdorff space. Let be the following statement: “a perfect -space with no more than clopen subsets is connectifiable if and only if no proper nonempty clopen subset of is feebly compact". In this note we show that neither nor is provable in ZFC.
An observation on Krull and derived dimensions of some topological lattices
Let , be an algebraic lattice. It is well-known that with its topological structure is topologically scattered if and only if is ordered scattered with respect to its algebraic structure. In this note we prove that, if is a distributive algebraic lattice in which every element is the infimum of finitely many primes, then has Krull-dimension if and only if has derived dimension. We also prove the same result for , the set of all prime elements of . Hence the dimensions on the lattice...
...-Applications dans une variété
Bi-Lipschitz embeddings into low-dimensional Euclidean spaces
Canonical embedding of function spaces into the topological bidual of .
Chainable continua and homeomorphisms of the plane onto itself
Closed embeddings into complements of -products
In some sense, a dual property to that of Valdivia compact is considered, namely the property to be embedded as a closed subspace into a complement of a -subproduct of a Tikhonov cube. All locally compact spaces are co-Valdivia spaces (and only those among metrizable spaces or spaces having countable type). There are paracompact non-locally compact co-Valdivia spaces. A possibly new type of ultrafilters lying in between P-ultrafilters and weak P-ultrafilters is introduced. Under Martin axiom and...
Collectionwise normality and extensions of continuous functions
Connectedness and local connectedness of topological groups and extensions
It is shown that both the free topological group and the free Abelian topological group on a connected locally connected space are locally connected. For the Graev’s modification of the groups and , the corresponding result is more symmetric: the groups and are connected and locally connected if is. However, the free (Abelian) totally bounded group (resp., ) is not locally connected no matter how “good” a space is. The above results imply that every non-trivial continuous homomorphism...
Containing spaces for planar rational compacta [Book]
Diagonals and discrete subsets of squares
In 2008 Juhász and Szentmiklóssy established that for every compact space there exists a discrete with . We generalize this result in two directions: the first one is to prove that the same holds for any Lindelöf -space and hence is -separable. We give an example of a countably compact space such that is not -separable. On the other hand, we show that for any Lindelöf -space there exists a discrete subset such that ; in particular, the diagonal is a retract of and the projection...