Baire Spaces and the Wijsman Topology
... This theorem was first given by J. Oxtoby in 1957. Then, it was re-discovered by M. R. Krom in 1974, and later on by J. Saint-Raymond in 1983. By a strategy for the player β, we mean a mapping defined for all finite sequences of moves of α. A winning strategy for β is a strategy which can be use ...
... This theorem was first given by J. Oxtoby in 1957. Then, it was re-discovered by M. R. Krom in 1974, and later on by J. Saint-Raymond in 1983. By a strategy for the player β, we mean a mapping defined for all finite sequences of moves of α. A winning strategy for β is a strategy which can be use ...
local contractibility, cell-like maps, and dimension
... if every continuous function from A' to a polyhedron is null homotopic. In addition, a continuous surjection /: X -» Y between compact spaces is called cell-like provided that f~l(y) has trivial shape for every y e Y. One of the most outstanding open problems in geometric topology is whether a cell- ...
... if every continuous function from A' to a polyhedron is null homotopic. In addition, a continuous surjection /: X -» Y between compact spaces is called cell-like provided that f~l(y) has trivial shape for every y e Y. One of the most outstanding open problems in geometric topology is whether a cell- ...
Topology Proceedings - topo.auburn.edu
... Hausdorff space together with a closed partial order. Associ ated are two significant topologies: the collection of all open upper sets is called the stably compact topology, and the col lection of all open lower sets is called the dual-stably compact topology. A space is stably compact if it is t ...
... Hausdorff space together with a closed partial order. Associ ated are two significant topologies: the collection of all open upper sets is called the stably compact topology, and the col lection of all open lower sets is called the dual-stably compact topology. A space is stably compact if it is t ...
Selected Old Open Problems in General Topology
... disconnected if the closure of every open subset of X is open. These spaces seem to be quite special. In particular, none of them contains a non-trivial convergent sequence. Therefore, only discrete extremally disconnected spaces are first-countable. Nevertheless, extremally disconnected spaces are ...
... disconnected if the closure of every open subset of X is open. These spaces seem to be quite special. In particular, none of them contains a non-trivial convergent sequence. Therefore, only discrete extremally disconnected spaces are first-countable. Nevertheless, extremally disconnected spaces are ...
Spring 2009 Topology Notes
... A for some A ∈ X} and the intersection X = {x : x ∈ A for all A ∈ X}. This is typically done when X is a collection of sets, but the definitions work even in the general case. It turns out that inconsistencies arise unless some restriction is placed on those properties P (x) which can be used to def ...
... A for some A ∈ X} and the intersection X = {x : x ∈ A for all A ∈ X}. This is typically done when X is a collection of sets, but the definitions work even in the general case. It turns out that inconsistencies arise unless some restriction is placed on those properties P (x) which can be used to def ...
A Discourse on Analytical Study of Nearly
... The concept of pre- open (i.e. þ-open), semi open (i.e. s-open), pre-semi open (i.e. α-open) and semipre open (i.e. β-open) sets plays an important role in the research of generalizations of continuity in topological spaces [1]. By using these sets many authors introduced and studied various types o ...
... The concept of pre- open (i.e. þ-open), semi open (i.e. s-open), pre-semi open (i.e. α-open) and semipre open (i.e. β-open) sets plays an important role in the research of generalizations of continuity in topological spaces [1]. By using these sets many authors introduced and studied various types o ...
