A generalisation of normal spaces
A generalization of Čech-complete spaces and Lindelöf -spaces
The class of -spaces is studied in detail. It includes, in particular, all Čech-complete spaces, Lindelöf -spaces, metrizable spaces with the weight , but countable non-metrizable spaces and some metrizable spaces are not in it. It is shown that -spaces are in a duality with Lindelöf -spaces: is an -space if and only if some (every) remainder of in a compactification is a Lindelöf -space [Arhangel’skii A.V., Remainders of metrizable and close to metrizable spaces, Fund. Math. 220 (2013),...
A Generalization of Chain-net Spaces
A generalization of -compact spaces
A generalization of Magill's Theorem for non-locally compact spaces
In the theory of compactifications, Magill's theorem that the continuous image of a remainder of a space is again a remainder is one of the most important theorems in the field. It is somewhat unfortunate that the theorem holds only in locally compact spaces. In fact, if all continuous images of a remainder are again remainders, then the space must be locally compact. This paper is a modification of Magill's result to more general spaces. This of course requires restrictions on the nature of the...
A generalization of N. Aronszajn's theorem on connectedness of the fixed point set of a compact mapping
A generalization of normal spaces
A new class of spaces which contains the class of all normal spaces is defined and its characterization and properties are discussed.
A generalization of Tychonoff's theorem
A generalization of -sets and -sets by means of operators associated with a topology and associated functions.
A generating family for the Freudenthal compactification of a class of rimcompact spaces
For X a Tikhonov space, let F(X) be the algebra of all real-valued continuous functions on X that assume only finitely many values outside some compact subset. We show that F(X) generates a compactification γX of X if and only if X has a base of open sets whose boundaries have compact neighborhoods, and we note that if this happens then γX is the Freudenthal compactification of X. For X Hausdorff and locally compact, we establish an isomorphism between the lattice of all subalgebras of and the...
A generic theorem in the theory of cardinal invariants of topological spaces
Relative versions of many important theorems on cardinal invariants of topological spaces are formulated and proved on the basis of a general technical result, which provides an algorithm for such proofs. New relative cardinal invariants are defined, and open problems are discussed.
A Geometric Approach to the Bohr Compactification of Cones.
A Hamiltonian property of connected sets in the alternative set theory.
A hedgehog in a product
A hereditarily normal strongly zero-dimensional space with a subspace of positive dimension and an N-compact space of positive dimension
A Hilbert cube compactification of the function space with the compact-open topology
Let X be an infinite, locally connected, locally compact separable metrizable space. The space C(X) of real-valued continuous functions defined on X with the compact-open topology is a separable Fréchet space, so it is homeomorphic to the psuedo-interior s = (−1, 1)ℕ of the Hilbert cube Q = [−1, 1]ℕ. In this paper, generalizing the Sakai-Uehara’s result to the non-compact case, we construct a natural compactification (X) of C(X) such that the pair ( (X), C(X)) is homeomorphic to (Q, s). In case...
A homogeneous space of point-countable but not of countable type
We construct an example of a homogeneous space which is of point-countable but not of countable type. This shows that a result of Pasynkov cannot be generalized from topological groups to homogeneous spaces.
A large -discrete Fréchet space having the Souslin property
A lattice of conditions on topological spaces II
A lemma on finite-dimensional covers