The Collaborative International Dictionary of English v.0.48:

Closeness \Close"ness\, n.
   The state of being close.
   [1913 Webster]

         Half stifled by the closeness of the room. --Swift.
   [1913 Webster]

         We rise not against the piercing judgment of Augustus,
         nor the extreme caution or closeness of Tiberius.
                                                  --Bacon.
   [1913 Webster]

         An affectation of closeness and covetousness.
                                                  --Addison.

   Syn: Narrowness; oppressiveness; strictness; secrecy;
        compactness; conciseness; nearness; intimacy; tightness;
        stinginess; literalness.
        [1913 Webster]

WordNet (r) 3.0 (2006):

closeness
    n 1: a feeling of being intimate and belonging together; "their
         closeness grew as the night wore on" [syn: closeness,
         intimacy]
    2: the quality of being close and poorly ventilated [syn:
       stuffiness, closeness]
    3: the spatial property resulting from a relatively small
       distance; "the sudden closeness of the dock sent him into
       action" [syn: nearness, closeness] [ant: farawayness,
       farness, remoteness]
    4: extreme stinginess [syn: meanness, minginess,
       niggardliness, niggardness, parsimony,
       parsimoniousness, tightness, tightfistedness,
       closeness]
    5: characterized by a lack of openness (especially about one's
       actions or purposes) [syn: closeness, secretiveness]
       [ant: nakedness, openness]
    6: close or warm friendship; "the absence of fences created a
       mysterious intimacy in which no one knew privacy" [syn:
       familiarity, intimacy, closeness]

Moby Thesaurus II by Grady Ward, 1.0:

175 Moby Thesaurus words for "closeness":
   THI, accord, accordance, addition, adjunct, affairs, affiliation,
   affinity, agreement, airlessness, airtight secrecy, alikeness,
   alliance, analogy, aping, approach, approximation, assemblage,
   assimilation, association, avarice, bond, cheapness, chumminess,
   close secrecy, closefistedness, combination, community,
   compactness, comparability, comparison, concealment, confinement,
   confines, conformity, congestedness, congestion, connectedness,
   connection, consistence, consistency, contiguity, contrariety,
   convergence, copying, correspondence, crowdedness, crypticness,
   dealings, deduction, denseness, density, discreetness, discretion,
   disjunction, environs, evasion, evasiveness, familiarity,
   filiation, firmness, foreground, gluiness, hair, hairbreadth,
   hairsbreadth, hardfistedness, hardness, hiddenness, hoarding,
   homology, hugger-mugger, hugger-muggery, humidity, humidness,
   identity, illiberality, imitation, immediacy, immediate foreground,
   impenetrability, impermeability, imporosity, incapaciousness,
   incommodiousness, incompressibility, indisposition to speak,
   inseparableness, intercourse, intimacy, intimate acquaintance,
   jammedness, junction, lack of meaning, lack of message, liaison,
   likeness, likening, limitation, link, linkage, linking, mateyness,
   meaninglessness, metaphor, mimicking, miserliness, mugginess,
   mutual attraction, narrow gauge, narrowness, nearness,
   neighborhood, nighness, oppression, oppressiveness, palliness,
   parallelism, parity, penny-pinching, precinct, propinquity,
   proximity, purlieus, rapport, relatedness, relation, relations,
   relationship, relative density, resemblance, restrictedness,
   restriction, sameness, secrecy, secretiveness, secretness,
   semblance, similarity, simile, similitude, simulation, slenderness,
   solidity, solidness, special affinity, specific gravity,
   spissitude, stickiness, stinginess, straitness, strictness,
   stuffiness, subterfuge, swelter, sympathy,
   temperature-humidity index, the dark, thickness, tie, tie-in,
   tight purse strings, tight squeeze, tightfistedness, tightness,
   uncommunicativeness, unconversableness, ungenerosity, union,
   unsociability, vicinage, vicinity, viscidity, viscosity,
   viscousness