## Classes of spaces defined by nested sequences of sets and maps among such spaces |

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### Contents

DEFINITIONS AND ASSORTED FACTS | 7 |

THE EFFECT OF SEPARATION AXIOMS | 35 |

PRODUCTS AND PERFECT PRE IMAGES | 49 |

2 other sections not shown

### Common terms and phrases

a k space accumulation point basic open set bi-k space bisequential spaces cf(a Chapter Chart cl(f Claim classes in columns classes of spaces classification theorems closed and discrete closed maps coding technique column G compact set containing the open converging countable space countably bisequential countably compact subsets disjoint union Example 3.7 Example 5.3 filter base accumulating Frechet spaces Hausdorff space iff whenever F limit point locally compact spaces locally conditionally compact locally countably compact map f meshes metric space normal space open image open maps open set containing order topology paracompact paracompact M space perfect preimage pointwise countable type Potential lemma product of countably proof of Theorem Property quotient maps regular spaces relatively countably bi-quasi-k relatively quasi-k space S-sequence separation axioms sequence of sets sequentially q sequentially quasi-k singly bi-k spaces of pointwise strict q space subspace technique successor ordinals Theorem 2.9 thesis U S(A ultrafilter