Given a 2D binary image it is sometimes of interest to determine invariant topological properties, such as Euler number and holes which can reflect directly the complexity of a binary image. Counting the number of holes of binary images is an important problem arising in medical image processing, phototypesetting, petroleum exploration, earthquake prediction, and pattern recognition. In this pa...

It is shown that certain weak-base structures on a topological space give a D-space. This solves the question by A.V. Arhangel’skii of when quotient images of metric spaces are D-spaces. A related result about symmetrizable spaces also answers a question of Arhangel’skii. Theorem. Any symmetrizable space X is a D-space (hereditarily). Hence, quotient mappings, with compact fibers, from metric s...

In this paper we give new proofs of the theorem of Maćkowiak and Tymchatyn that every metric continuum is a weakly-confluent image of some one-dimensional hereditarily indecomposable continuum of countable weight. The first is a model-theoretic argument; the second is a topological proof inspired by the first.

A Hausdorff topological space X is called superconnected (resp. coregular ) if for any nonempty open sets U 1 , … n ⊆ the intersection of their closures ‾ ∩ not empty complement ∖ ( a regular space). canonical example projective Q P ∞ vector < ω = { x ∈ : | ≠ 0 } over field rationals . The quotient by equivalence relation ∼ y iff ⋅ We prove that every countable second-countable homeomorphic to ...

We prove that if a paratopological group G is a continuous image of an arbitrary product of regular Lindelöf Σ-spaces, then it is R-factorizable and has countable cellularity. If in addition, G is regular, then it is totally ω-narrow and satisfies celω(G) ≤ ω, and the Hewitt–Nachbin completion of G is again an R-factorizable paratopological group.

A space $Y$ is called an {em extension} of a space $X$, if $Y$ contains $X$ as a dense subspace. Two extensions of $X$ are said to be {em equivalent}, if there is a homeomorphism between them which fixes $X$ point-wise. For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Yleq Y'$, if there is a continuous function of $Y'$ into $Y$ which fixes $X$ point-wise. An extension $Y$ ...