一般拓扑

We show that for each element $g$ of a Garside group, there exists a positive integer $m$ such that $g^m$ is conjugate to a periodically geodesic element $h$, an element with $|h^n|_\D=|n|\cdot|h|_\D$ for all integers $n$, where $|g|_\D$…

Assuming PFA, every uncountable subset E of the plane meets some C^1 arc in an uncountable set. This is not provable from MA(aleph_1), although in the case that E is analytic, this is a ZFC result. The result is false in ZFC for C^2 arcs,…

It is proved that any infinite Abelian group of infinite exponent admits a non-discrete reflexive group topology.

We investigate Baire-one functions whose graph is contained in a graph of usco mapping. We prove in particular that such a function defined on a metric space with values in $\mathbb{R}^d$ is the pointwise limit of a sequence of continuous…

This dissertation investigates the relative complexity between a continuum and its proper subcontinua, in particular, providing examples of atriodic n-od-like continua. Let X be a continuum and n be an integer greater than or equal to…

A duality theorem for the category of locally compact Hausdorff spaces and continuous maps which generalizes the well-known Duality Theorem of de Vries is proved.

For a locally path connected topological space, the topological fundamental group is discrete if and only if the space is semilocally simply-connected. While functoriality of the topological fundamental group for arbitrary topological…

The notion of a regular operator with compact supports between function spaces is introduced. On that base we obtain a characterization of absolute extensors for zero-dimensional spaces in terms of regular extension operators having compact…

Contents: 1. Editor's note 2. Research announcements 2.1. Pseudocompact group topologies with no infinite compact subsets 2.2. Selective coideals on (FIN[1]k) 2.3. Entire functions mapping uncountable dense sets of reals onto each other…

Let $T$ be a tree with a fixed subset of vertices $V^{\ast}$ such that there is a cyclic order $C$ on it and all terminal vertices are contained in this set. Let $D^{2} = \{(x,y) \in \rr^{2} | x^{2} + y^{2} \leq 1 \}$ be a closed oriented…

We determine the Lusternik-Schnirelmann category of the irreducible, symmetric Riemann spaces SU(n)/SO(n) and SU(2n)/Sp(n) of type AI and AII respectively.

If a discrete subset S of a topological group G with the identity 1 generates a dense subgroup of G and S \cup {1} is closed in G, then S is called a suitable set for G. We apply Michael's selection theorem to offer a direct,…

In this note we shall prove that the Stone-\v{C}ech compactification of $\mathcal{L}^n$ is the space $\bar{\mathcal{L}}^n$ where $\bar{\mathcal{L}}$ is the extended long line, namely, $\mathcal{L}$ together with its ends $\pm \Omega$. We…

In a separably connected space any two points are contained in a separable connected subset. We show a mechanism that takes a connected bounded metric space and produces a complete connected metric space whose separablewise components form…

We consider fixed points of the Feigenbaum (periodic-doubling) operator whose orders tend to infinity. It is known that the hyperbolic dimension of their Julia sets go to 2. We prove that the Lebesgue measure of these Julia sets tend to…

In the present paper, the Lindelof number and the degree of compactness of spaces and of the cozero-dimensional kernel of paracompact spaces are characterized in terms of selections of lower semi-continuous closed-valued mappings into…

In this article we introduce the concept of limit space and fundamental limit space for the so-called closed injected systems of topological spaces. We present the main results on existence and uniqueness of limit spaces and several…

Given a closed orientable surface (\Sigma) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (\Sigma) and the convex compact set of additive functions on…

S. Garcia-Ferreira and H. Ohta gave a construction that was intended to produce a tau-pseudocompact space, which has a regular-closed zero set A and a regular-closed C-embedded set B such that neither A nor B is tau-pseudocompact. We show…

This collection of thirty two reviewed articles covers several fields of General Topology. Several contributions represent invited presentations at the Ninth Prague Topological Symposium.