Some similarity between contractions and Kannan mappings.
Some topological consequences of the Product Measure Extension Axiom
Some versions of second countability of metric spaces in ZF and their role to compactness
In the realm of metric spaces we show in ZF that: (i) A metric space is compact if and only if it is countably compact and for every , every cover by open balls of radius has a countable subcover. (ii) Every second countable metric space has a countable base consisting of open balls if and only if the axiom of countable choice restricted to subsets of holds true. (iii) A countably compact metric space is separable if and only if it is second countable.
Some weak forms of continuity in bitopological spaces
Space structures, their theory and application. II.
Spaces of ANR's
Spaces of ANR's. II
Spaces of retractions which are homeomorphic to Hilbert space
Spaces of Seminorms.
Spaces whose only finite-sheeted covers are themselves. I.
Spaces with a locally countable -network.
Spaces with a primitive base and perfect mappings
Spaces with countable -networks
In this paper, we prove that a space is a sequentially-quotient -image of a metric space if and only if has a point-star -network consisting of -covers. By this result, we prove that a space is a sequentially-quotient -image of a separable metric space if and only if has a countable -network, if and only if is a sequentially-quotient compact image of a separable metric space; this answers a question raised by Shou Lin affirmatively. We also obtain some results on spaces with countable...
Spaces with property
We prove that if is a first countable space with property and with a -diagonal then the cardinality of is at most . We also show that if is a first countable, DCCC, normal space then the extent of is at most .
Spaces with -locally countable weak-bases
In this paper, spaces with -locally countable weak-bases are characterized as the weakly open msss-images of metric spaces (or -first countable spaces with -locally countable -networks).
Spaces With -Locally Finite Lindelöf sn-Networks
Spaces with -weakly hereditarily closure-preserving sn-networks.
Spaces without Large Projective Subspaces.
Special bases for compact metrizable spaces
Squares of Q sets