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Compact productivity of Lindelöf-type properties
A subclass of the class of feebly Lindelöf spaces, namely the almost cellular-Lindelöf spaces, which contains the class of all cellular-Lindelöf...
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The closed finite-to-one map**s and their applications
In this paper, we discuss the closed finite-to-one map** theorems on generalized metric spaces and their applications. It is proved that point- G δ ...
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Cellular-compact spaces and their applications
We introduce the notion of a cellular-compact space and prove that cellular compactness is a nice property that implies cellular Lindelöfness. The...
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Maximal densely countably compact topologies
A topological space X is densely countably compact if it possesses a dense subspace D with the property that every infinite subset of D has an...
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On relaxations of contraction constants and Caristi’s theorem in b-metric spaces
In this paper, the following facts are stated in the setting of b -metric spaces.
(1) The contraction constant in the Banach contraction principle...
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Maximal countably compact spaces and embeddings in MP-spaces
We study embeddings in maximal pseudocompact spaces together with maximal countable compactness in the class of Tychonoff spaces. It is proved that...
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B-saturated Hull Classes in ℓ-groups and Covering Classes of Spaces
W denotes the category of archimedean ℓ -groups with designated weak unit and ℓ -homomorphisms that preserve the weak unit, and B is the bounded...
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Maximal pseudocompact spaces and the Preiss-Simon property
We study maximal pseudocompact spaces calling them also MP-spaces. We show that the product of a maximal pseudocompact space and a countable compact...
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On hull classes of ℓ-groups and covering classes of spaces
W denotes the category of archimedean ℓ -groups with designated weak unit and ℓ -homomorphisms that preserve the weak unit. Comp denotes the category...
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Supercomplete topological spaces
Supercomplete topological spaces and other variants of supercompleteness are defined in this paper. The main idea is to give different...
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Well-Embedding and G δ -Density in a Pointfree Setting
Translating the notion of G δ -dense and well-embedded subspaces into a pointfree setting gives some elegant results (with remarkably simple proofs),...
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Productively Fréchet Spaces
We solve the long standing problem of characterizing the class of strongly Fréchet spaces whose product with every strongly Fréchet space is also...
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Products of Quasi-p-Pseudocompact Spaces
Given p ∈β (ω) ω, we determine when a product of quasi- p -pseudocompact spaces preserves this property. In particular, we analyze the product of quasi-
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Ultracomplete Topological Spaces
In 1987 V. I. Ponomarev and V. V. Tkachuk characterized strongly complete topological spaces as those spaces which have countable character in their...
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Sobriety in Terms of Nets
Sobriety is a subtle notion of completeness for topological spaces: A space is sober if it may be reconstructed from the lattice of its open subsets....
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On θ-Principal Extension and H-Closedness
A type of extensions called the θ-extention of topological spaces and their θ-equivalence and θ-trace systems are introduced, which ultimately...
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