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... A topological space X is said to be weakly countably compact (or limit point compact) if every infinite subset of X has a limit point. Every countably compact space is weakly countably compact. The converse is true in T1 spaces. A metric space is weakly countably compact if and only if it is compact ...
... A topological space X is said to be weakly countably compact (or limit point compact) if every infinite subset of X has a limit point. Every countably compact space is weakly countably compact. The converse is true in T1 spaces. A metric space is weakly countably compact if and only if it is compact ...
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... Proposition 1. Any first countable topological space is compactly generated. Proof. Suppose X is first countable, and A ⊆ X has the property that, if C is any compact set in X, the set A ∩ C is closed in C. We want to show tht A is closed in X. Since X is first countable, this is equivalent to showi ...
... Proposition 1. Any first countable topological space is compactly generated. Proof. Suppose X is first countable, and A ⊆ X has the property that, if C is any compact set in X, the set A ∩ C is closed in C. We want to show tht A is closed in X. Since X is first countable, this is equivalent to showi ...
On Some Maps Concerning gα-Open Sets
... Definition 2.3. Let (X, τ ) and (Y, σ) be topological spaces. A map f : (X, τ ) → (Y, σ) is said to have an α-closed graph if its G(f) = {(x, y) : y = f (x), x ∈ X} is α-closed in the product space (X × Y, τp ), where τp denotes the product topology. It is well-known that the graph G(f ) of f is a c ...
... Definition 2.3. Let (X, τ ) and (Y, σ) be topological spaces. A map f : (X, τ ) → (Y, σ) is said to have an α-closed graph if its G(f) = {(x, y) : y = f (x), x ∈ X} is α-closed in the product space (X × Y, τp ), where τp denotes the product topology. It is well-known that the graph G(f ) of f is a c ...
(1) g(S) c u,
... total order. First some examples. Let X be a totally ordered set which is a connected space in the interval topology, let £ be a subset of X containing, with t, all elements less than t, and letbe any continuous
function from X into (0, 1) whose restriction,
0O, to £ is a strictly
order-preservi ...
... total order. First some examples. Let X be a totally ordered set which is a connected space in the interval topology, let £ be a subset of X containing, with t, all elements less than t, and let
SUBSPACES OF PSEUDORADIAL SPACES Martin Sleziak 1
... If, moreover, for each i ∈ I the coreflective hereditary kernel of Ai is FG, then, obviously, the coreflective hereditary kernel of A is again FG. Corollary 4.3. A = CH({S α ; α ∈ Cn}) is the smallest coreflective subcategory of Top such that SA = Top. Obviously, the coreflective hereditary kernel o ...
... If, moreover, for each i ∈ I the coreflective hereditary kernel of Ai is FG, then, obviously, the coreflective hereditary kernel of A is again FG. Corollary 4.3. A = CH({S α ; α ∈ Cn}) is the smallest coreflective subcategory of Top such that SA = Top. Obviously, the coreflective hereditary kernel o ...