Topological Space Objects in a Topos II: ...-Completeness and ...-Cocompleteness.
Topological spaces compact with respect to a set of filters
If is a family of filters over some set I, a topological space X is sequencewise -compact if for every I-indexed sequence of elements of X there is such that the sequence has an F-limit point. Countable compactness, sequential compactness, initial κ-compactness, [λ; µ]-compactness, the Menger and Rothberger properties can all be expressed in terms of sequencewise -compactness for appropriate choices of . We show that sequencewise -compactness is preserved under taking products if and only if there...
Topological spaces with a selected subset-cardinal invariants and inequalities
Cardinal functions for topological spaces in which a subset is selected in a certain way are defined and studied. Most of the main cardinal inequalities are generalized for such spaces.
Topological Structures On Classes I
Topological structures on classes I.
Topological Structures On Classes II
Topological structures on classes II.
Topological structures on classes III.
Topologically maximal convergences, accessibility, and covering maps
Topologically maximal pretopologies, paratopologies and pseudotopologies are characterized in terms of various accessibility properties. Thanks to recent convergence-theoretic descriptions of miscellaneous quotient maps (in terms of topological, pretopological, paratopological and pseudotopological projections), the quotient characterizations of accessibility (in particular, those of G. T. Whyburn and F. Siwiec) are shown to be instances of a single general theorem. Convergence-theoretic characterizations...
Topologically maximal pretopologies
Topologické prostory
Topologie combinatoire et invariants combinatoires
Topologie fine et mesure de référence.
Topologie générale et espaces d'ultrafiltres
Topologie su spazi di funzioni derivanti da topologie su iperspazi
Topologies generated by closed intervals.
Topologies generated by ideals
A topological space is said to be generated by an ideal if for all and all there is in such that , and is said to be weakly generated by if whenever a subset of contains for every with , then itself is closed. An important class of examples are the so called weakly discretely generated spaces (which include sequential, scattered and compact Hausdorff spaces). Another paradigmatic example is the class of Alexandroff spaces which corresponds to spaces generated by finite sets....
Topologies on free monoids induced by families of languages
Topology from Neighbourhoods
Using Mizar [9], and the formal topological space structure (FMT_Space_Str) [19], we introduce the three U-FMT conditions (U-FMT filter, U-FMT with point and U-FMT local) similar to those VI, VII, VIII and VIV of the proposition 2 in [10]: If to each element x of a set X there corresponds a set B(x) of subsets of X such that the properties VI, VII, VIII and VIV are satisfied, then there is a unique topological structure on X such that, for each x ∈ X, B(x) is the set of neighborhoods of x in this...
Topology in a category: Compactness.